pg-slow-gin.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# GIN Index O(N^2) Lookup\n",
    "\n",
    "I ran into an issue with using the && array operator on a GIN index of mine. Basically I have a query that looks like this:\n",
    "\n",
    "```sql\n",
    "SELECT * FROM example WHERE keys && ARRAY[...];\n",
    "```\n",
    "\n",
    "This works fine for a small number of array elements (N), but gets really slow as N gets bigger in what appears to be O(N^2) complexity.\n",
    "\n",
    "\n",
    "However, from studying the GIN data structure as described by the docs, it seems that the performance for this could be O(N). In fact, it's possible to coerce the query planner into an O(N) plan like this:\n",
    "\n",
    "```sql\n",
    "SELECT DISTINCT ON (example.id) * FROM unnest(ARRAY[...]) key JOIN example ON keys && ARRAY[key]\n",
    "```\n",
    "\n",
    "The notebook below demonstrates this issue."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Requirement already satisfied: psycopg2-binary in /usr/local/lib/python3.7/site-packages (2.7.5)\n",
      "Requirement already satisfied: pandas in /usr/local/lib/python3.7/site-packages (0.23.4)\n",
      "Requirement already satisfied: pytz>=2011k in /usr/local/lib/python3.7/site-packages (from pandas) (2018.5)\n",
      "Requirement already satisfied: python-dateutil>=2.5.0 in /usr/local/lib/python3.7/site-packages (from pandas) (2.7.3)\n",
      "Requirement already satisfied: numpy>=1.9.0 in /usr/local/lib/python3.7/site-packages (from pandas) (1.15.1)\n",
      "Requirement already satisfied: six>=1.5 in /usr/local/lib/python3.7/site-packages (from python-dateutil>=2.5.0->pandas) (1.11.0)\n",
      "Requirement already satisfied: matplotlib in /usr/local/lib/python3.7/site-packages (2.2.3)\n",
      "Requirement already satisfied: six>=1.10 in /usr/local/lib/python3.7/site-packages (from matplotlib) (1.11.0)\n",
      "Requirement already satisfied: python-dateutil>=2.1 in /usr/local/lib/python3.7/site-packages (from matplotlib) (2.7.3)\n",
      "Requirement already satisfied: kiwisolver>=1.0.1 in /usr/local/lib/python3.7/site-packages (from matplotlib) (1.0.1)\n",
      "Requirement already satisfied: cycler>=0.10 in /usr/local/lib/python3.7/site-packages (from matplotlib) (0.10.0)\n",
      "Requirement already satisfied: pytz in /usr/local/lib/python3.7/site-packages (from matplotlib) (2018.5)\n",
      "Requirement already satisfied: numpy>=1.7.1 in /usr/local/lib/python3.7/site-packages (from matplotlib) (1.15.1)\n",
      "Requirement already satisfied: pyparsing!=2.0.4,!=2.1.2,!=2.1.6,>=2.0.1 in /usr/local/lib/python3.7/site-packages (from matplotlib) (2.2.0)\n",
      "Requirement already satisfied: setuptools in /usr/local/lib/python3.7/site-packages (from kiwisolver>=1.0.1->matplotlib) (40.0.0)\n",
      "Requirement already satisfied: numpy in /usr/local/lib/python3.7/site-packages (1.15.1)\n"
     ]
    }
   ],
   "source": [
    "# Install dependencies\n",
    "!pip3 install psycopg2-binary\n",
    "!pip3 install pandas\n",
    "!pip3 install matplotlib\n",
    "!pip3 install numpy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import modules and setup matplotlib inlining and pandas row display options\n",
    "%matplotlib inline\n",
    "import psycopg2\n",
    "import pandas as pd\n",
    "import re\n",
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "pd.set_option('display.max_rows', 20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Connect to our database: you may change this DSN if you're not using the supplied docker-compose file.\n",
    "# We also set autocommit to True so we can run VACUUUM (which is non-transactional) below.\n",
    "pg_dsn = 'postgres://postgres@localhost:9999/postgres'\n",
    "conn = psycopg2.connect(pg_dsn)\n",
    "conn.autocommit = True\n",
    "cur = conn.cursor()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>id</th>\n",
       "      <th>keys</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>[1, 2, 3]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>[4, 5, 6]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>[7, 8, 9]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>[10, 11, 12]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>[13, 14, 15]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>6</td>\n",
       "      <td>[16, 17, 18]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>7</td>\n",
       "      <td>[19, 20, 21]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>8</td>\n",
       "      <td>[22, 23, 24]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>9</td>\n",
       "      <td>[25, 26, 27]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>10</td>\n",
       "      <td>[28, 29, 30]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99990</th>\n",
       "      <td>99991</td>\n",
       "      <td>[299971, 299972, 299973]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99991</th>\n",
       "      <td>99992</td>\n",
       "      <td>[299974, 299975, 299976]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99992</th>\n",
       "      <td>99993</td>\n",
       "      <td>[299977, 299978, 299979]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99993</th>\n",
       "      <td>99994</td>\n",
       "      <td>[299980, 299981, 299982]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99994</th>\n",
       "      <td>99995</td>\n",
       "      <td>[299983, 299984, 299985]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99995</th>\n",
       "      <td>99996</td>\n",
       "      <td>[299986, 299987, 299988]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99996</th>\n",
       "      <td>99997</td>\n",
       "      <td>[299989, 299990, 299991]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99997</th>\n",
       "      <td>99998</td>\n",
       "      <td>[299992, 299993, 299994]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99998</th>\n",
       "      <td>99999</td>\n",
       "      <td>[299995, 299996, 299997]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99999</th>\n",
       "      <td>100000</td>\n",
       "      <td>[299998, 299999, 300000]</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>100000 rows × 2 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "           id                      keys\n",
       "0           1                 [1, 2, 3]\n",
       "1           2                 [4, 5, 6]\n",
       "2           3                 [7, 8, 9]\n",
       "3           4              [10, 11, 12]\n",
       "4           5              [13, 14, 15]\n",
       "5           6              [16, 17, 18]\n",
       "6           7              [19, 20, 21]\n",
       "7           8              [22, 23, 24]\n",
       "8           9              [25, 26, 27]\n",
       "9          10              [28, 29, 30]\n",
       "...       ...                       ...\n",
       "99990   99991  [299971, 299972, 299973]\n",
       "99991   99992  [299974, 299975, 299976]\n",
       "99992   99993  [299977, 299978, 299979]\n",
       "99993   99994  [299980, 299981, 299982]\n",
       "99994   99995  [299983, 299984, 299985]\n",
       "99995   99996  [299986, 299987, 299988]\n",
       "99996   99997  [299989, 299990, 299991]\n",
       "99997   99998  [299992, 299993, 299994]\n",
       "99998   99999  [299995, 299996, 299997]\n",
       "99999  100000  [299998, 299999, 300000]\n",
       "\n",
       "[100000 rows x 2 columns]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create a table with lots of rows and array elements. You can see the data in the table below.\n",
    "rows = 100000\n",
    "keys_per_row = 3\n",
    "\n",
    "cur.execute(\"\"\"\n",
    "DROP SCHEMA IF EXISTS gin CASCADE;\n",
    "CREATE SCHEMA gin;\n",
    "SET search_path = gin;\n",
    "\n",
    "CREATE TABLE example AS\n",
    "SELECT \n",
    "\ta AS id,\n",
    "\tarray_agg((a-1)*%s+b) AS keys\n",
    "FROM\n",
    "\tgenerate_series(1, %s) a,\n",
    "\tgenerate_series(1, %s) b\n",
    "GROUP BY 1;\n",
    "CREATE INDEX ON example USING GIN (keys) WITH (fastupdate = off);\n",
    "\"\"\", (keys_per_row, rows, keys_per_row))\n",
    "cur.execute('VACUUM ANALYZE example')\n",
    "\n",
    "pd.read_sql_query('SELECT * from example ORDER BY id ASC', con=conn)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# The two queries we'll benchmark. query_1 is the main query we are interested in. query_2 produces the same result\n",
    "# and is included for comparison.\n",
    "query_1 = \"EXPLAIN ANALYZE SELECT * FROM example WHERE keys && %s\"\n",
    "query_2 = \"EXPLAIN ANALYZE SELECT DISTINCT ON (example.id) * FROM unnest(%s) key JOIN example ON keys && ARRAY[key]\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "EXPLAIN ANALYZE SELECT * FROM example WHERE keys && %s\n",
      "Bitmap Heap Scan on example  (cost=51.57..924.35 rows=1493 width=37) (actual time=0.031..0.034 rows=1 loops=1)\n",
      "  Recheck Cond: (keys && '{1,2,3}'::integer[])\n",
      "  Heap Blocks: exact=1\n",
      "  ->  Bitmap Index Scan on example_keys_idx  (cost=0.00..51.19 rows=1493 width=0) (actual time=0.016..0.016 rows=1 loops=1)\n",
      "        Index Cond: (keys && '{1,2,3}'::integer[])\n",
      "Planning time: 0.095 ms\n",
      "Execution time: 0.070 ms\n",
      "\n",
      "\n",
      "EXPLAIN ANALYZE SELECT DISTINCT ON (example.id) * FROM unnest(%s) key JOIN example ON keys && ARRAY[key]\n",
      "Unique  (cost=18850.84..19350.84 rows=100000 width=45) (actual time=0.191..0.222 rows=1 loops=1)\n",
      "  ->  Sort  (cost=18850.84..19100.84 rows=100000 width=45) (actual time=0.182..0.195 rows=3 loops=1)\n",
      "        Sort Key: example.id\n",
      "        Sort Method: quicksort  Memory: 25kB\n",
      "        ->  Nested Loop  (cost=18.99..7469.52 rows=100000 width=45) (actual time=0.052..0.155 rows=3 loops=1)\n",
      "              ->  Function Scan on unnest key  (cost=0.00..1.00 rows=100 width=4) (actual time=0.009..0.022 rows=3 loops=1)\n",
      "              ->  Bitmap Heap Scan on example  (cost=18.99..64.69 rows=1000 width=37) (actual time=0.020..0.024 rows=1 loops=3)\n",
      "                    Recheck Cond: (keys && ARRAY[key.key])\n",
      "                    Heap Blocks: exact=3\n",
      "                    ->  Bitmap Index Scan on example_keys_idx  (cost=0.00..18.74 rows=1000 width=0) (actual time=0.009..0.009 rows=1 loops=3)\n",
      "                          Index Cond: (keys && ARRAY[key.key])\n",
      "Planning time: 0.151 ms\n",
      "Execution time: 0.269 ms\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Force the query planner to use our gin index, even if it would prefer a seqscan and show \n",
    "# the query plans for the queries we're testing elow. \n",
    "cur.execute(\"SET enable_seqscan=false\")\n",
    "\n",
    "# Show the query plans for our two queries\n",
    "for q in [query_1, query_2]:\n",
    "    cur.execute(q, ([1,2,3],))\n",
    "    print(q+'\\n'+'\\n'.join([x[0] for x in cur.fetchall()])+'\\n\\n')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>keys</th>\n",
       "      <th>time_1</th>\n",
       "      <th>time_2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>100</td>\n",
       "      <td>0.739</td>\n",
       "      <td>6.407</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>200</td>\n",
       "      <td>1.559</td>\n",
       "      <td>14.393</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>300</td>\n",
       "      <td>2.478</td>\n",
       "      <td>20.422</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>400</td>\n",
       "      <td>3.443</td>\n",
       "      <td>24.321</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>500</td>\n",
       "      <td>5.052</td>\n",
       "      <td>25.884</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>600</td>\n",
       "      <td>5.090</td>\n",
       "      <td>28.320</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>700</td>\n",
       "      <td>7.025</td>\n",
       "      <td>42.164</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>800</td>\n",
       "      <td>10.705</td>\n",
       "      <td>49.854</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>900</td>\n",
       "      <td>13.036</td>\n",
       "      <td>47.125</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>1000</td>\n",
       "      <td>11.391</td>\n",
       "      <td>44.917</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>190</th>\n",
       "      <td>19100</td>\n",
       "      <td>3301.329</td>\n",
       "      <td>764.326</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>191</th>\n",
       "      <td>19200</td>\n",
       "      <td>3329.506</td>\n",
       "      <td>769.577</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>192</th>\n",
       "      <td>19300</td>\n",
       "      <td>3390.567</td>\n",
       "      <td>772.412</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>193</th>\n",
       "      <td>19400</td>\n",
       "      <td>3384.921</td>\n",
       "      <td>772.484</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>194</th>\n",
       "      <td>19500</td>\n",
       "      <td>3454.552</td>\n",
       "      <td>782.037</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>195</th>\n",
       "      <td>19600</td>\n",
       "      <td>3431.758</td>\n",
       "      <td>773.164</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>196</th>\n",
       "      <td>19700</td>\n",
       "      <td>3484.491</td>\n",
       "      <td>792.020</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>197</th>\n",
       "      <td>19800</td>\n",
       "      <td>3525.461</td>\n",
       "      <td>795.225</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>198</th>\n",
       "      <td>19900</td>\n",
       "      <td>3534.550</td>\n",
       "      <td>817.695</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>199</th>\n",
       "      <td>20000</td>\n",
       "      <td>3697.944</td>\n",
       "      <td>802.012</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>200 rows × 3 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      keys    time_1   time_2\n",
       "0      100     0.739    6.407\n",
       "1      200     1.559   14.393\n",
       "2      300     2.478   20.422\n",
       "3      400     3.443   24.321\n",
       "4      500     5.052   25.884\n",
       "5      600     5.090   28.320\n",
       "6      700     7.025   42.164\n",
       "7      800    10.705   49.854\n",
       "8      900    13.036   47.125\n",
       "9     1000    11.391   44.917\n",
       "..     ...       ...      ...\n",
       "190  19100  3301.329  764.326\n",
       "191  19200  3329.506  769.577\n",
       "192  19300  3390.567  772.412\n",
       "193  19400  3384.921  772.484\n",
       "194  19500  3454.552  782.037\n",
       "195  19600  3431.758  773.164\n",
       "196  19700  3484.491  792.020\n",
       "197  19800  3525.461  795.225\n",
       "198  19900  3534.550  817.695\n",
       "199  20000  3697.944  802.012\n",
       "\n",
       "[200 rows x 3 columns]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Run our benchmark, basically just running the queries from above with an increasing amount of elements in the\n",
    "# array we're performing an overlap operation with.\n",
    "step = 100\n",
    "steps = 200\n",
    "results = []\n",
    "\n",
    "def gin_query(sql, args):\n",
    "    cur.execute(sql, args)\n",
    "    plan = '\\n'.join([x[0] for x in cur.fetchall()])\n",
    "    \n",
    "    # make sure all our queries used our GIN index\n",
    "    if plan.find('Index Scan') < 0:\n",
    "        raise Exception(\"unexpected query plan\")\n",
    "    time = float(re.search('Execution time: ([0-9.]+)', plan, flags=re.IGNORECASE)[1])\n",
    "    return time\n",
    "\n",
    "\n",
    "for p in range(steps):\n",
    "    keys = [k+1 for k in range(step * (p+1))]\n",
    "    time_1 = gin_query(query_1, (keys,))\n",
    "    time_2 = gin_query(query_2, (keys,))\n",
    "\n",
    "    result = (len(keys), time_1, time_2)\n",
    "    results.append(result)\n",
    "\n",
    "df = pd.DataFrame(results, columns=[\"keys\", \"time_1\", \"time_2\"])\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1103d9860>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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S1M1yObjgAqipgSeegI03ThUXhT4VhQqMTKay56xm5exhIUmSJElSv5PLwcEHw267wc9+Bo88ksKJKVOK10QaG+1X0RkrLCRJkiRJ6kZ33VUMKz72sRRKNDVBa6tjTFeHFRaSJEmSJHWTt96C559PFRQf+1hxvRBO1NYWx5gWpoOofVZYSJIkSZLUDd5+OzXNPOUU2HTTtu+VjjGdNi09l/a00MqssJAkSZIkqYs6Gkf65z/Dc8/BySevHFZAGlda2rOicE2kudkqi46EGGOlz9DtampqYktLS6WPIUmSJEnqY0orJbLZ9Hq//WDkSLjiCth88+K+5mbHlLYnhLAgxljT2T6vhEiSJEmS1EWFyojaWpg6NU0DGTkSFi6Exx5LexxZ2j28EiJJkiRJ0mrIZovTPjIZmDMHHn/ckaXdzQoLSZIkSZJWQy4HF1yQwopFi1JYURpiOLK0exhYSJIkSZLURblcugayxx5w1VXpUVsLs2alyorCyFKnf6w9r4RIkiRJktRFf/lLCivOPRc+/vH0mDIl9bOYNy9VVmSzbRtzas1YYSFJkiRJUhcsWQIvvADnnAOf+ERxvbW1GFZA25GlWnOONZUkSZIkqR0NDalPRTYL774LJ54Iu+wCTz/tuNK14VhTSZIkSZLWQiaTrnbcdFMxrPjOdxxX2lMMLCRJkiRJakc2C5dfDvvvD8uXp7DCvhQ9x8BCkiRJkqR2LF0K118PRx8NP/2p40p7moGFJEmSJEmknhWFcaRLl6Y+FRtsAL/8peNKK8HAQpIkSZIkij0rbr459ax4//thxgyYNi09mprS+4YWPcPAQpIkSZLU55VWTxRez5qVnkvtvz+MHZtGlZ53HsycCRMnpvccV9qzDCwkSZIkSX1eoXqiEFoMHAiTJqVnSOsHHwz//nfqWXH++XDCCcWwoiCbdaRpTxlY6QNIkiRJklRuheqI2trUPLOxMVVPzJgBr74KF1wAe+wBBx2UpoEUelZkszbarBQDC0mSJElSv5DNprBi+vQUSEycmMKK6dOLFRj//d/F0aXZbFpzlGllGFhIkiRJkvqFXC5VTRSqJzbZJFVWZDKwaFF6vzScKO1ZYWDR8wwsJEmSJEl9Xi7Xtlpik01Sj4pdd01rjz6a3j/00Laf80pI5dh0U5IkSZLU5zU3t62eeOst+PznYc89YbPNnABSjaywkCRJkiT1eaWTPd54A557Dq6+Gj760eK61RTVxcBCkiRJktRvvP46TJkCp58OQ4ZU+jRaFQMLSZIkSVK/8NprKayYNg0+/OFKn0adsYeFJEmSJKlXa2hITTVL5XJpveDVV1NYccYZhhW9hYGFJEmSJKlXy2TShI9CaFGYCJLJpNevvAInnwxnngkf+lDlzqnVY2AhSZIkSerVChM+amth6lQYPTpVU2Sz8PLLcOqpMGoU/PznlT6pVoc9LCRJkiRJvV42C3V1MH06fO1rMGMGDBsGN98MX/4yHHFECjXUe1hhIUmSJEnq9XI5aGyE+nq44Qb49rfhK1+BjTYqhhWOLO1drLCQJEmSJPUaDQ2pN0Vp+DBrVroKMm9eWt9+e/jqV+GAA9L++nrDit7ICgtJkiRJUq/RXoPN+vo0qjSbhWefhVtuKQYY9fWp8mLFKSKqflZYSJIkSZJ6jdIGm3V1KYyYPz+tL14MP/xharr59a8XKy6y2bTfayG9ixUWkiRJkqRepbTBZl1dev2Pf8CPfgRnnQUPPtg2nCiEHM3NlT23Vo8VFpIkSZKkXqW0wWZjI2y9NbS0wMyZ8L73weTJK3+mUGmh3sPAQpIkSZLUa+Ryba93fOpTcMwxcN11KaxQ3+GVEEmSJElSr9HcXAwr/vY3eOSR1KvivvsqfTJ1NyssJEmSJEm9RuG6R0sLXHMNzJgB66wD/+//VfZc6n4GFpIkSZKkqtTQkMaYlvaeyOVg7lz4yEfgjDMghMqdT+XllRBJkiRJUlXKZFK/ilwuvc7l4IAD4N134bTTDCv6OgMLSZIkSVJVKowjra2FqVNTWPGVr8DFFxtW9AcGFpIkSZKkqpXNQl0dTJ8On/tcGmOq/sHAQpIkSZJUtXI5OPdc2G8/WLCgeD1EfZ+BhSRJkiSpKuVyMHYsfOtbMH9+8XqIoUX/YGAhSZIkSapKF1wA3/0u/PCH6XWhp0Vzc2XPpZ7hWFNJkiRJUtX52c/gsMNg/Pi269ls2zGn6rsMLCRJkiRJVaGhIY0yfeAB2HLL1Lcil0sVFZMnV/p06mleCZEkSZIk9biGhpV7UQwYAPvsA+++WwwramtTiKH+xwoLSZIkSVKPy2RSGNHUlK543HILTJ0KxxyTwow33kgjTAvvq/8xsJAkSZIk9bhCA83aWviv/4Kzz4azzoLjjoPBg2H6dKivN6zoz7wSIkmSJEmqiGwWJkyAM86Aww9PYUUulyor6uvTsyNM+y8rLCRJkiRJFXHzzamyYsIEuOoq2GYbmDGjeA0km217bUT9ixUWkiRJkqSyW7HJ5h/+AKNHw/77pxGmTU2pqmLKlGI4Ubg20txcmTOrssoWWIQQ1gsh3BNC+FsI4eEQwvfz68NCCH8NISwKIVwRQhiUX39f/vWi/PtDS75rSn790RDCPuU6syRJkiSpPApNNnM5ePNNmDgRBg1K1RWQwon586G1te3nsllHmvZX5aywWALsFWPcHtgB2DeEsAvwI+CcGOOWwL+Bo/L7jwL+nV8/J7+PEMJw4FDgs8C+wAUhhAFlPLckSZIkqZsVqiUOOgj23BOefx6uu67tVQ/DCZUqW2ARkzfzL9fNPyKwF3Blfv1S4ID8z/vnX5N//4shhJBfnxNjXBJjfBJYBOxUrnNLkiRJkspj+HD41KdgwYLUYNO+FFqVsvawCCEMCCHcD/wLuBn4X+DVGGOhyGcxsHn+582BpwHy778GDC5db+czpb/r2BBCSwih5cUXXyzHnyNJkiRJWkP//Ge6/vHkk04AUdeUNbCIMS6LMe4AbEGqivg/ZfxdF8UYa2KMNUOGDCnXr5EkSZIkrabHH4fvfQ/uvBPmzoVp09L1kEJPC6k9PTIlJMb4KpADPgdsEkIojFPdAngm//MzwMcB8u9vDLxcut7OZyRJkiRJVeyBB+Cii6CmJoUVTgBRVw3sfMuaCSEMAZbGGF8NIbwf+BKpkWYOOAiYA3wD+F3+I9flX/8l//4tMcYYQrgO+E0IYRawGbAVcE+5zi1JkiRJ6h5//SvMmwc/+hGs087/XZ7N2sdCHStbYAFsClyan+ixDtAUY5wfQlgIzAkhnAHcB8zO758N/CqEsAh4hTQZhBjjwyGEJmAh0AocF2NcVsZzS5IkSZLWQkMDDBwIb78N06dDCOnqR3OzU0DUdWULLGKMDwAj2ll/gnamfMQY3wEO7uC7zgTO7O4zSpIkSZK637JlqU/FvHnFsKK2Nl0BkbqqnBUWkiRJkqR+pqkJBg9OYUVtLdTVpYkgTU1e/9DqMbCQJEmSJHWLX/4SBg2CY49Nr+vq0pWQ+nrDCq2+HpkSIkmSJEnq284/HzbZBA4/PL3O5VJlRX19enZ8qVaXgYUkSZIkqcsaGtqGDzHChAlw330wblxaK+1ZMW1aeq6tNbTQ6jGwkCRJkiR1WSZTDB9ihCOOgCuuKFZWQJoGUtqzIptNr5ubK3Nm9U72sJAkSZIkdVkhfDj4YPjMZ+Dee+HMM9v2qMhkUjhRupbN2sdCq8cKC0mSJEnSavn852HLLeHPf07BxYwZxesehesgmUxlz6jez8BCkiRJktRlb74Jhx4Kjz2WGmrecANMmZJCiqlTi70rrKbQ2vJKiCRJkiSpS15+GY46Cu64A666qnjNo7YWRo1yhKm6lxUWkiRJkqROPfNMqqAYORKuvLJtQ80pU+Dqqx1hqu5lhYUkSZIkaZUeewwuuADOPhvWW6/te7lc6mExb17biguvhWhtWWEhSZIkSerQvffC7Nkwc+bKYQU4wlTlE2KMlT5Dt6upqYktLS2VPoYkSZIk9Wq33ZYep54K6/h/d6ubhBAWxBhrOtvnf+QkSZIkSSu57rpUVbHbbm3DilwOGhoqdy71HwYWkiRJkqQ2fv1reOklmDgRDjmk2EQzl0v9KTKZyp5P/YNNNyVJkiRJ7zn/fPjYx+CrX02vm5pSSFFXlyaA2ExTPcUKC0mSJEkSMaZpH5/5DBx4YHE9m01hxfTp6dmwQj3FwEKSJEmS+rlly1JjzWefhQED2r43a1Z61NenCovC9RCp3AwsJEmSJKkfamhI4cOSJXDiiXD44TBsGIwZUwwlZs2CSZNg2rT0KFwPMbRQTzCwkCRJkqR+KJOBgw+GQw+F734XXnghXQmZNi2FElOnpqqKmTNT801I10GamqC5ubJnV/9g001JkiRJ6oe22w523RVuvx1mz27bUPPVV1PPivr6YlhRkM3ax0I9wwoLSZIkSerjCtc/ChYvhqOOgh13hOOOa9tQM5dL4YU9K1RpBhaSJEmS1MdlMsXeE489lq6A3HknbLhh23Bi1qy0r6nJnhWqPK+ESJIkSVIfV+g9MW4cfPaz8OijcPLJqWdF4RpINgujR6dqi8KVj9KeFV4DUU+zwkKSJEmS+oGlS2HkSPjzn+Fb34LW1mJYAel5/vy0XiqbhcmTe/68koGFJEmSJFWpFXtPQHrd0LB63/Pb38INN8CDDxavf2QyK1dNGE6omhhYSJIkSVKVKu09Aem5tjatd9X558Pf/w6//rW9KdS7GFhIkiRJUpUq9JCorYWpU4sNMbvST2L58hRObLMNbLDBytc/Cr0ppGplYCFJkiRJVSybTSNHS0ePdmbGDPjKV2DMGNhrr+I1j9KrJF7/ULUzsJAkSZKkKpbLtR092tk1jjffhHvugZtugldfLX7H6l4lkSrNsaaSJEmSVKUKQUPp6NFVXQv517/g9NPhwgvh4YfT3rq6FHR09SqJVC2ssJAkSZKkKtXc3PXeE08+ma6NNDTARz6yZldJpGoSYoyVPkO3q6mpiS0tLZU+hiRJkiT1iPvvh8svhzPPhEGD0lqhOsMKC1WbEMKCGGNNZ/ussJAkSZKkXqShoW0fi1tugfPOg8GDVw4rHGOq3szAQpIkSZJ6kUymGD5ceSVcey3Mnw8771zcszpXSaRqZdNNSZIkSepFCuHDmDGw997whz+kPhWl1z0ymRROlK4VmnZKvYUVFpIkSZLUi8QId98N++8P11wDBx4IM2YUr3s4wlR9hYGFJEmSJPUSra0wZQpssgncdBPU18MNN6S12lqYOnXVY0+l3sQrIZIkSZLUC7z1VgomdtwRTjihGEpksymkGDUqXQ2przesUN9ghYUkSZIkVcCK0z4gvW5oWHnvyy/DpElw0knw/PMrN9ScMgWuvjqFFY2NTgNR32BgIUmSJEkVUDrtAzruPfHkk3DaaalPxaabwuTJbSsocrn03rx5jjBV32JgIUmSJEkVUJj2sareEy0tqWJi1izYeOP2v8cRpuqrQoyx0mfodjU1NbGlpaXSx5AkSZKkTk2dWuw9MW1acf2GG+Bvf4P/+R8IoXLnk7pbCGFBjLGms31WWEiSJElSheRyqYJixd4Tl1wCzz2XelYYVqi/MrCQJEmSpDJrr8HmrFkwZky6vlHoPbHffjB6NAwZAkcemfZ11IhT6usMLCRJkiSpzNprsFm4AlLoPbHbbrDLLvCnP8H66xf3tdeIU+oPBlb6AJIkSZLU1zQ0pJBhxdGjY8bAxInp+sf8+cX3X38dTjkFfv5z+Oc/U0hRV5f2rdiIU+ovrLCQJEmSpG7WXkXFjBkwfnxqsFlXVwwhnn02hRmnnQaf/nRar6tbeZ/U3xhYSJIkSVI3a29k6ZQpafJHaYPNhx+Gs86CmTPhwx9On+2oEafU33glRJIkSZLKoLRS4mtfSxUWhesd2SyMGwf77w+/+AUMGJA+U+hZUbqv9LXUn1hhIUmSJElrob0JILkcTJhQrJS46qpUYVEIHV56Cb7+dRg+vBhWADQ3tw0nCpUazc0987dI1STEGCt9hm5XU1MTW1paKn0MSZIkSf3AilURuRwccACEANdcU1yrrYUrroCFC+EjH0mvpf4ohLAgxljT2T4rLCRl/CiRAAAgAElEQVRJkiRpLbTXr+LQQ4thRWHPb38LP/gB/N//a1ghdYU9LCRJkiRpLZX2q6ivh2nT2r7/9tvw+9/DeefBZz9bmTNKvY0VFpIkSZK0llY12eOll2DSJDjxRMMKaXVYYSFJkiRJa2FVkz0++Uk455w0IeQDH6j0SaXexcBCkiRJktZCR5M9rrwSNtoIZs2Cddet7Bml3qhsV0JCCB8PIeRCCAtDCA+HEL6bXz89hPBMCOH+/OPLJZ+ZEkJYFEJ4NISwT8n6vvm1RSGEk8p1ZkmSJEnqzIpjTCdPLq4XvPIKbLllqqwwrJDWTDl7WLQCJ8QYhwO7AMeFEIbn3zsnxrhD/nE9QP69Q4HPAvsCF4QQBoQQBgDnA6OA4cBhJd8jSZIkST0qk0lXPgqhReFKSCYDMcKPfwytrfC976XRppLWTNmuhMQYnwOey//8RgjhEWDzVXxkf2BOjHEJ8GQIYRGwU/69RTHGJwBCCHPyexeW6+ySJEmS1JHSMaZ1danJZlMT7LYbnHoqjBqVfpa0dnpkSkgIYSgwAvhrfunbIYQHQgi/CCF8ML+2OfB0yccW59c6WpckSZKkiigdY1pXBzvuCCecAN/8pmGF1F3KHliEEDYErgKOjzG+DjQCnwZ2IFVgnN1Nv+fYEEJLCKHlxRdf7I6vlCRJkqR2lY4x/elP4etfh9NOg622qvTJpL6jrIFFCGFdUlhxeYzxaoAY4wsxxmUxxuXAzyle+3gG+HjJx7fIr3W03kaM8aIYY02MsWbIkCHd/8dIkiRJEm3HmO6/P3zpS3DnnfDAA5U+mdS3lHNKSABmA4/EGGeVrG9asm0c8FD+5+uAQ0MI7wshDAO2Au4BmoGtQgjDQgiDSI05ryvXuSVJkiRpVQpjTN98E/70J5gzB+bOTeuSuk/Zmm4CuwJfAx4MIdyfXzuZNOVjByACTwETAGKMD4cQmkjNNFuB42KMywBCCN8G/gAMAH4RY3y4jOeWJEmSpA5Nngw/+xlssEFxpGk2mx6Suk+IMVb6DN2upqYmtrS0VPoYkiRJknq5hoY0rrQQRixbBkccAeutBxddVNmzSb1VCGFBjLGms309MiVEkiRJknqjTCb1q8jl0hWQ2lqYNw8OO6zSJ5P6vnJeCZEkSZKkXi2bTf0qDjwQPv1peOIJuPpqr39IPcEKC0mSJElahcGDYeutoaUFjjvOsELqKQYWkiRJktSBG2+Ec8+FRYugvh4aG9P1EEnlZ2AhSZIkSaQGm6VhxOzZ8Mtfpishc+fCtGnp50JPC0nlZWAhSZIkSRQbbP7xjzB9Orz0Esyfn4KKwjWQQk+L5ubKnlXqD2y6KUmSJEmkMOLSS2HMGPj611NzzfnzV+5Zkc3ax0LqCVZYSJIkSRLw9NPw+9/Dt74FF10EdXUGE1IlGVhIkiRJ6vfuuQfOOw/GjoXLLrPBplQNvBIiSZIkqV+bOxf++U/48pfhkENSj4rCtY/a2uJrST3LCgtJkiRJ/VKMcNZZEAKccAK0tLQNJ2ywKVVWiDFW+gzdrqamJra0tFT6GJIkSZKq1DvvwKmnpoqKTKbSp5H6lxDCghhjTWf7vBIiSZIkqc9paEhBRKFaoqEBBg6E1tY0AWTaNNhzz9SjwsBCqk5eCZEkSZLU52Qyqf9EoWnmwIEwaRL861/wox/B6NFwxBFpvVQul8INSZVnYCFJkiSpzyn0n6ithalTYcYMOPLINPljww3hG9+A6dPTeiHUyOXSfisupOrglRBJkiRJfVI2C3V1KZjYd1/4whdgs83S6/p6mDgRRoxIIUVdXQoznAgiVQ8rLCRJkiT1SbkcXHABfP7z8Je/wIsvplCivj4953JtQ426OsMKqZoYWEiSJEnqc3I5OOgg2G03+NWv0rWQSZNgypTUcLNwXWTWrJVDDEnVwSshkiRJkvqc66+HPfaASy6BjTdO00FmzkzPkCoppkxJQca8eel1NptCDK+FSNXBwEKSJElSn/KnP8H73w9z5xangEyevPK+1tZiWAHFRp3NzQYWUjUIMcZKn6Hb1dTUxJaWlkofQ5IkSVIPmz0bli+HY46p9EkkdSSEsCDGWNPZPissJEmSJPVqDQ0wciTccQfsuivsvXfqRdHc3H5lhaTewaabkiRJknq1z3wGxoyBT3+6GFbU1kImU+mTSVobVlhIkiRJ6rUWLkw9K5qa4MgjYdGiNO3DxplS72dgIUmSJKlqNTSkSonS8KFw3WP4cLj/fjjnHBgwAOrqYPr0NKLUsELq/bwSIkmSJKlqZTLpekcul15PmAD77w///Ce89hqceircfntab2xMYUVjY3G/pN7LCgtJkiRJVaG9agqA8eNTaFFXB7/9LSxZkqorDj88BRMHHAAhwDXXpM9ms2m/10Kk3s0KC0mSJElVYcVqikLzzEMPLV73+Mxn4Fe/gtNOg6lTi+8XwgpIz01N6dqIpN4rxBgrfYZuV1NTE1taWip9DEmSJEmrqRBS1NUVm2cCjBuXqioeewzmzk37Cv0qpk2r7JklrZ4QwoIYY01n+6ywkCRJklQ1stliNUVdXVobOxa++lW4664UVhxwAPz4x/arkPo6AwtJkiRJVSOXKzbPvOACOPFEOPlk+OlPU58KSM+HHJIqK5qa2l4jkdR32HRTkiRJUlUoXAdpaoIRI+Chh9LaLrsU9zQ3d9yvwgabUt/SaYVFCKEhhPCBEMK6IYQ/hRBeDCF8tScOJ0mSJKlvaGhYuQoil0vrBc3NKXzYbLNUYXHxxXD11W2bZ06evHIwkc2mdUl9S1euhOwdY3wdGA08BWwJnFjOQ0mSJEnqWzqaAJLJFPdMngzvvptGl55zDnzoQ4YRUn/WlSshhT37AXNjjK+FwuUxSZIkSeqCwtWNFSeAFKolYoTzz4cNN4TTT6/oUSVVia5UWMwPIfwd2BH4UwhhCPBOeY8lSZIkqa9ZcQJIIax45x046aTUt+Kb36zoESVVkU4DixjjScDngZoY41LgP8D+5T6YJEmSpL6ldAJIYRzps8/CCSfAccfBrrtW+oSSqkmnV0JCCAOA3YChIYTS/bPKdipJkiRJfUrpBJBsNj1GjYLPfQ6uvx7e//7ivuZm+1ZI6tqVkHnAN4HBwEYlD0mSJEnqksIEkGw29av43/+F/faDe+6Bu+9Oe9prxCmp/+pK080tYozblf0kkiRJkvqsQsXEkiXw/e/Dl74EV11VDCnaa8QpqX/rSoXFDSGEvct+EkmSJEl92jPPwMSJMGFCMZToqBGnJHUlsLgbuCaE8HYI4fUQwhshhNfLfTBJkiRJ1aehIVVFlMrl0vqq9t11V2quudlm8MlPtv3sio04JQm6FljMAj4HrB9j/ECMcaMY4wfKfC5JkiRJVSiTSVc4CsFCR30nCvtuuQUuvhjmzoU//hE+//nintJGnNOmpefS75bUv3UlsHgaeCjGGMt9GEmSJEnVLZstBgtTp7ad/LHivl//GkaPhttvh8svT6FF6b7SRpyl393c3HN/j6Tq1ZWmm08At4YQbgCWFBZjjI41lSRJkvqh0r4T9fXt95145hm47jo4+mj4yU/a39fe6NLCyFNJ6kqFxZPAn4BBONZUkiRJ6vc66ztx551w3nkwZgz89rf2p5C0ZjqtsIgxfr8nDiJJkiSp+pX2nShUQxRe77ln6lfR2gr77guHHNL+PisoJHVFVyosJEmSJAnouO/EX/4Cp5wCW26Zrou0tNifQtLaCX2xl2ZNTU1saWmp9DEkSZKkfuGZZ+AHP0g9KUpHlkpSe0IIC2KMNZ3t60rTTUmSJElq1513puaaM2fC+99f6dNI6ks6DSxCCEOAY4ChpftjjEeW71iSJEmSqlmMxX4VgwfD3Xe37U2Ry6XrH+1NApGkruhKD4vfARsDfwR+X/KQJEmS1A+9/TZMmQJbbZX6Vey0U2qoWZgCUmjMmclU9pySereuXAlZP8b4P2U/iSRJkqSq98QTMGtWCiw23zytFRpq1tamAKOx0WkgktZeVyos5ocQvlz2k0iSJEmqOg0NxcqJG26ASy6BsWPh8svb7stmU1gxfXp6NqyQtLa6Elh8lxRavB1CeD2E8EYI4fVyH0ySJElS5WUycPDBMGECvPJKCiIOP3zl6x65XKqsqK9Pz4WQQ5LWVKdXQmKMG/XEQSRJkiRVn+23hy98IV3x+OhH4fjjV77uUehZUVjPZtu+lqQ10WGFRQjh/+SfR7b36LkjSpIkSeoJpdc/AO67D445BrbbDv77vzu+7tHc3DacKPS0aG7uubNL6ntWVWExETgWOLud9yKwV1lOJEmSJKkiMpliZcQzz8Bdd8Ftt8Guu8KMGcXrHoUqioL2RpeuuEeSVleHFRYxxmPzz9l2Hp2GFSGEj4cQciGEhSGEh0MI382vfyiEcHMI4fH88wfz6yGE8OMQwqIQwgOlVRwhhG/k9z8eQvjG2v/ZkiRJklaUzcKvfw377ZcabF55JZx8cgormppg2rTiNBB7VEgqt6403VxTrcAJMcbhwC7AcSGE4cBJwJ9ijFsBf8q/BhgFbJV/HAs0Qgo4gNOAnYGdgNMKIYckSZKk7rN4McybB0cfDb/5Tbr+0drqdQ9JlVG2wCLG+FyM8d78z28AjwCbA/sDl+a3XQockP95f+CymNwNbBJC2BTYB7g5xvhKjPHfwM3AvuU6tyRJktRflPasuOUWOP98+PjH4Re/KF7/yGRWvtqRzbZ/DUSSulM5KyzeE0IYCowA/gp8NMb4XP6t54GP5n/eHHi65GOL82sdra/4O44NIbSEEFpefPHFbj2/JEmS1BcVRpZ++9vwj3/AkCEwZUq6+uH1D0mV1qXAIoSweQjh8yGEPQqPrv6CEMKGwFXA8THG10vfizFGUgPPtRZjvCjGWBNjrBkyZEh3fKUkSZLUp40YAXvuCZdfDk8+maoqZs6EiRPT+17/kFRJq5oSAkAI4UfAIcBCYFl+OQK3d+Gz65LCistjjFfnl18IIWwaY3wuf+XjX/n1Z4CPl3x8i/zaM8CeK6zf2tnvliRJktSxe++Fyy6Diy6Cc89NI0vr64thRYHTPiRVSlcqLA4APhNj/HKMcUz+MbazD4UQAjAbeCTGOKvkreuAwqSPbwC/K1n/en5ayC7Aa/mrI38A9g4hfDDfbHPv/JokSZKkLir0q4gx9ai4/XYYMyZdAWlsLPas8PqHpGrRaYUF8ASwLrBkNb97V+BrwIMhhPvzaycDPwSaQghHAf8AavPvXQ98GVgEvAUcARBjfCWEMB0oFKJNizG+sppnkSRJkvqNhoaVm2UOHAijR8PYsTBhQgouDjgAQoBrrilWUtTWtp0KIkmVElIbiVVsCOEqYHvSCNL3QosY43fKe7Q1V1NTE1taWip9DEmSJKkicrm2wUMuBwceCMOHwyOPwHHHpWqK8ePh0EPbhhO5XOpZ4RQQSeUSQlgQY6zpbF9XKiyuyz8kSZIk9QKFZpm1tVBXl3pUHHwwXHhhmv5R6FcxbVr7n7W6QlI16DSwiDFeGkIYBGydX3o0xri0vMeSJEmStDayWTj22BRO1NbC7NmpeqK0X4XhhKRq1mnTzRDCnsDjwPnABcBjqzPWVJIkSVLPu+IKmDULvv1tuOWW9HPhmsi0acUKDJtsSqpWXZkScjawd4zxCzHGPYB9gHPKeyxJkiRJXVWYAFL6+hvfgK98BX7ykxRO1NeniSCFiorCtZHm5va/U5IqrSs9LNaNMT5aeBFjfCyEsG4ZzyRJkiSpAx1NABkzBq69Fu67D268Ed73PvjqV9P72SzMn79yOOGVEEnVrCsVFi0hhItDCHvmHz8HHMEhSZIkVUAm0/YqRy4HM2bAiSem0GLRInjwwRRelIYR2ayTPyT1Ll0JLOqAhcB38o+F+TVJkiRJZbbidY9sNl3tGDMGpk5N4cUpp8Cbb8J3vgMXXZQmg1g5Iam36zSwiDEuiTHOijGOzz/OiTEu6YnDSZIkSf1dRxUV48enCSA77AAf+ACMGgW/+EVxAojNNCX1dh0GFiGEpvzzgyGEB1Z89NwRJUmSpP6r0ByztrZYUTFlCvz+9ynMaGmBV1+FQw5xAoikvmVVTTe/m38e3RMHkSRJktS+bDZd85g+Hb72tRRK7LMPXHxxCixGj07vtTcBxKshknqrDissYozP5X/8VozxH6UP4Fs9czxJkiRJuVy65nHqqTBnTgor5syBjTYqTgBpbW37GZtsSurtutJ080vtrI3q7oNIkiRJWlkul653XHQRvPYanH8+3HIL3HprcY/hhKS+qMMrISGEOlIlxadW6FmxEXBXuQ8mSZIkKV3rOOUUuOsuOOOM1GBzyy297iGp71tVD4vfADcAM4CTStbfiDG+UtZTSZIkSWL5clh3XdhwQzjrLAghrWezhhWS+r5V9bB4Lcb4VIzxsHzfireBCGwYQvhEj51QkiRJ6icaGoqTPV58EY4/PoUVr7xSDCskqb/otIdFCGFMCOFx4EngNuApUuWFJEmSpDVUGk4UDBwIY8bAeefBD38Ie+8NJ5+cxpdKUn/TlaabZwC7AI/FGIcBXwTuLuupJEmSpD4uk0nNNAuhRS4HP/hBuupx6qmw/vpwxBFpPKnXPyT1R10JLJbGGF8G1gkhrBNjzAE1ZT6XJEmS1KdlsymMqK2FqVPhwANht91gxgz43vdSg826OsMKSf1XVwKLV0MIGwK3A5eHEM4D/lPeY0mSJEl9XzabQonp02H4cPjNb1LvisZGqK9PzyteG5Gk/qIrgcX+wFvA94Abgf8FxpTzUJIkSVJ/cNNNcPbZMH48PPoo/OxnqeKiqQmmTStWYBhaSOqPVjXWlBDCAGB+jDELLAcu7ZFTSZIkSX3cr38NxxwDF18Mhx+eQonRo1O1ReEaSOHaSHOzV0Mk9T+rDCxijMtCCMtDCBvHGF/rqUNJkiRJfdkVV8Bll8HvfpcmgUAKJObPT+FEqWzWsEJS/7TKwCLvTeDBEMLNlPSuiDF+p2ynkiRJkvqg//wnNdPcffd0HWRFhhOSVNSVwOLq/EOSJEnSGnrwQbjoIpgyBTbbrNKnkaTq12lgEWO0b4UkSZK0GhoaIJNJ1RIxwuzZsGABfPKThhWS1FWdTgkJITwZQnhixUdPHE6SJEnqjTKZNN1j3jyYNCldBbnsMhg0qO2+XC6FG5KklXVlrGkNkMk/dgd+DPy6nIeSJEmSerNsFurrU2ixzjqpb8X06TBjRnFEaS6X3s9kKntWSapWnQYWMcaXSx7PxBjPBfbrgbNJkiRJvU5ra6qa2GCDVF0xcybU1cHEiWlEaW0tTJ2anpuabLIpSR3ptIdFCGFkyct1SBUXXWnWKUmSJPUrTz2VAorjjoPnn4eTTkqVFo2NxQkgdXWp2qK+3rBCklalK8HD2SU/twJPAbVlOY0kSZJU5UobahbkcnDxxbD11nD22fDnP7etoMhm0+spU1J4sWKIIUlaWVemhPhfoZIkSVJeoaFmIYz4/e/h4IPTNY+TTkp7mpvbXvfIZlNYMXVqasRZGmJ4LUSS2tdhYBFCmLiqD8YYZ3X/cSRJkqTqls0We1Hsvz9cfjkcdBDsvHNxz+TJxQkgkyentdbWYlhR+j3NzQYWktSeVVVYbJR//gxpQsh1+ddjgHvKeShJkiSpmn3hCzByJMyeDaeeCnvt1bZaojABpKmp+JlCcFHKKyGS1LEOA4sY4/cBQgi3AyNjjG/kX58O/L5HTidJkiRVmWefhW9/G+65p9iLYq+9ilUXdXVpzasekrR2utJ086PAuyWv382vSZIkSf3KvHlwxRVw++1w9dUr96JwAogkdZ91urDnMuCeEMLp+eqKvwKXlPNQkiRJUjV5663UMLO1FbbbDubOXbkXxZw5bSeA5HKVPbMk9XZdmRJyZgjhBmD3/NIRMcb7ynssSZIkqee1N7L0oovg0ktTKLH55h1/9uqrVx5j6rUQSVpzXamwIMZ4b4zxvPzDsEKSJEl9UmFkaS4Hy5bBccelfhXjxrUNKwoTQAraG2NamAAiSVozIcZY6TN0u5qamtjS0lLpY0iSJKkXyuXgwANhyy3h8cfTFY8ZM9qfAGL1hCStvhDCghhjTWf7utJ0U5IkSeo3Xngh9am47bYUVkycCCNGOAFEknpap1dCQgj/HUL4YE8cRpIkSSqXhoaVG2GWXu149VWYPBmefhoefrht88xstjgBpK7OsEKSekJXelh8FGgOITSFEPYNIYRyH0qSJEnqbqX9KQAmTIADDkjrt92WwoiNNoLvfz9VUEyblp5ra2HWLCeASFJP61IPi3xIsTdwBFADNAGzY4z/W97jrRl7WEiSJKk9hf4TdXVw3nlp7aCD4AtfgC22gDFjUnAxcWLxM7NmpZGm8+bZw0KSukNXe1h0dUpIBJ7PP1qBDwJXhhAaVvlBSZIkqYqUXu34yldgr73gmmtg0SI45BCYP79tWAHQ2loMKwrf4QQQSSq/TissQgjfBb4OvARcDFwbY1waQlgHeDzG+OnyH3P1WGEhSZKk9uRycPDBsPPOcOut8Lvfwe23pwCjvj5dA5EklVd3Tgn5IDA+xviP0sUY4/IQwug1PaAkSZLUkwrjSrPZ1Fxz0qTUwyKEYm+KbNZrHpJULVZ5JSSEMAA4dMWwoiDG+EhZTiVJkiR1s9mzYfRouOyyVGEBKaw45JC2DTZtqClJ1WGVgUWMcRnwaAjhEz10HkmSJKlbvfIKnHgifO1rKazYYIO03tyc+ldceGF6bW8KSaouXelhcTswArgH+E9hPcY4trxHW3P2sJAkSerfGhrSuNKlS+Hmm2HKFPjb31IYMXlypU8nSf1bd/awqO+G80iSJEk9ZtttYb/9UmXFWWe1HUUqSeodOg0sYoy3hRA+CWwVY/xjCGF9YED5jyZJkiStvrvvhj/8AS69FL71LYgxNdRsarKhpiT1Jp0GFiGEY4BjgQ8BnwY2B34GfLG8R5MkSZK67t13YdYs+PCH4dxzU0PNBx8sjiw1rJCk3mWVTTfzjgN2BV4HiDE+DnyknIeSJEmSVsfEienKx4EHwtFHp7Bi1qz0KIwsdfqHJPUuXQkslsQY3y28CCEMBFbdqVOSJEnqAcuXw09/Cu+8A3feCYsXp/VZs2DSpDSu1JGlktQ7daXp5m0hhJOB94cQvgR8C5hX3mNJkiRJ7StMABk2DM4+G446Cj77WVi2LIUSdXVpfebMVHkBbUeWejVEknqHrgQWJwFHAQ8CE4DrgYvLeShJkiSpIzU1MHYsHHwwXHAB/OUvxQkgH/1osWdFIawoyGYNKySpN+nKlJDlwM/zD0mSJKlinn4arr0WZsyA7/9/9u47PKoy//v4+yC/FVEhNLFRXQtlUSRRUUBGBBWI1ISggquuIOJaAupmJVESNBKTKK4S0Wd1BYUQqrR1WcywVDHBghQLGkRFsYKiIETu5487Z1omMNS0z+u6ciVz5syZM+wfaz75lrFw9tn+DSBgf3ZnViigEBGp3CLZElJEmJkVxpiWx+SORERERERKuO0fXbvC5Mnw2WfQsyesW2dbP9xqCvBXWbhBReBjERGpfCIZuhkNxJR8dQaeBl452Iscx3nRcZxvHMdZH3DsEcdxvnQc592Sr54BzyU5jrPZcZwPHce5JuD4tSXHNjuO87dD+XAiIiIiUrnFxNjNH3Fx0LIldO4MQ4ZAzZrB1RS5ucHhRODMChERqZwiaQn5PuTQU47jrAVSDvLSfwHPAJNDjj9pjMkMPOA4TmsgAWgDnAkscRznvJKnnwW6A18ABY7jzDPGbDzYfYuIiIhI5WYMfPUVxMbCwoXQurUNJ5KSbEtIaDVFQkLw69USIiJSuR20wsJxnIsDvqIdx7mDyIKOZcAPEd5HHyDXGPObMaYI2AxcUvK12Rjzaclq1dySc0VERESkCtu+HUaNgtNPh5dfhjvvtO0fI0ZAcbGqKUREqoNItoRkBfxcDGwB4o/gPe9yHGcoUAiMMsb8CJwFvBlwzhclxwA+Dzl+abiLOo4zDBgG0LRp0yO4PREREREpLxkZ8MsvdkXp2LFw6qmQnW2/3PaPcHMpVE0hIlL1HLTCwhjjCfjqboy53Rjz4WG+Xw5wDnAR8BXBYcgRMcY8b4yJNsZEN2rU6GhdVkRERESOk+++g8JCeOop6NbNH1aMHg2pqfYrL8+2f3i95X23IiJyrEWyJSTxQM8bY7IjfTNjzPaA674ALCh5+CXQJODUs0uOcYDjIiIiIlJFzJ0La9bA88/DO+/YUGLECMjKgsxMSCz5L9LA9g9VVIiIVG2RtIS4W0LmlTyOBd4CPj7UN3Mc5wxjzFclD/sB7gaRecBUx3GysUM3zy15Dwc413GcFtigIgG44VDfV0REREQqnowMOO88WLkSrrzSDtL0em0YEbiyNDHkz2dq/xARqR4iCSzOBi42xvwMdjUpsNAYc9OBXuQ4zjSgK9DQcZwvgIeBro7jXAQY7CyM4QDGmA2O4+QBG7FzMkYaY34vuc5dwH+AE4AXjTEbDvEzioiIiEgF9OuvcMMNMH069O5tw4r4eLsFJHBlqQIKEZHqyTHGHPgEx/kQaGeM+a3k8YnAOmPM+cfh/g5LdHS0KSwsLO/bEBEREZEAGRkQE2PXk2ZkwDXXwPr1kJJiqyjCrSx1Q4xwgzZFRKRychxnrTEm+mDnRVJhMRl4y3GcOSWP+wL/OoJ7ExEREZFqKDoarr8e+vaFiRPtgM30dOjf39/+caCVpQosRESql4NWWAA4jnMx0Lnk4TJjzDvH9K6OkCosRERERA6PWwXhhgMZGVCzpg0SHnjAHnPnTLiPI/Hll/DEE9C0qQ0pRowIrqhwH6uSQkSk6juaFRYYY94G3j7iuxIRERGRCi0mJrgFo2ZNu1Y0M9M+7/XaeRNpaf7XHCjUuP9+mDwZtmyBRx+Fk9PnkKgAACAASURBVE+GHTvs64cMCW7/8HjU/iEiIn41yvsGRERERKTicFsw4uPtbIn0dBtWpKfbx/HxNmxwN3qAP9SoWfKnMHfuRNOmcO+98Mc/wsMP27DC6/UP1Jw1y1ZYhGv/EBERiajCQkRERESqD4+n9FpRtyrCfdy+vQ0l3FYON9TYscPOp7j5Zti8GR5/HE46yV43dICmW1HRvn1waKHqChERAQUWIiIiIhIisAoiJweiosKvGS0r1IiJgUGD4JJLgq9bUKCBmiIiEjkFFiIiIiLiE1oFERXln2GRmOivikhKCg4x6tSB7Gy46ip47z345ZfS1w43pFMVFSIiUhbNsBARERERn9AqiOJiG1YUF9vHHo8NK1JS7Hmpqbb94/77bcXFG2/AjBl2MGd2dvC1vV47oFNERCQSqrAQEREREZ/QKohwVRHFxTB/PnTsaGdUbN5sV5bu32+f93hsa0hKin8+RWDlhoiISCQcY0x538NRFx0dbQoLC8v7NkRERESqrOXL7ZaPe++F5s3Dn+OGFO5gTq0rFRERAMdx1hpjog92niosRERERCRiP/1kqynOPx+efBIcp+xzQwdzKqwQEZFDocBCRERERCIyf76trBg9Gk477eDnh24b0YBNERE5FBq6KSIiIiIHtH27DSkcxw7NjDSscGdWpKba7/Hx9riIiEgkVGEhIiIiImEZA1Om2KGaKSl2dWmkQreNeDz2cUGBqixERCQyGropIiIiIqUUFcFTT0FcHHTqVN53IyIiVYmGboqIiIjIIdu3D559Fn77DcaPh1q1yvuORESkulJgISIiIiIArFkDr7wCd94JrVqV992IiEh1p8BCREREpJr76SfIzIQWLWDCBKihsewiIlIBKLAQERERqaaMgTlzbGVFYiI0blzedyQiIuKn/FxERESkGtq6FUaNglNOsbMqFFaIiEhFo8BCREREpJrIyIAlS+xQzVdegXHj4P/+zx4XERGpaBRYiIiIiFQTdetCbKzd/PH3v8N990HfvhAT4z/H61WAISIiFYNmWIiIiIhUQRkZNojweGDXLsjKssM1hwyBv/0NPvsMcnPBcfyv8XohPh7y8srvvkVERFwKLERERESqoJgYGz7ccw/s2AGXXQYjRtgw4vTTIS0NkpNtoBEfb5/LybHPezzlffciIiJqCRERERGpklq0gK5d4YknoHZtf1gBNphITrbfwT6Xlma/K6wQEZGKQhUWIiIiIlXI3r12qObevTB5MqSn+6spwN/y4fHYr759bVuIG2C4x0VERMqbAgsRERGRKmLpUpgzB0aOhPPOszMpAqsptm8v3fLhODBoEKSm+ttD1BYiIiIVgVpCRERERI6BjAwbGAQ6nA0ckVwnORkGD7aBxFNP2bAiO9tuBMnLs2FEXh7Mnh18nYICG3BMmmQfezz2vIKCQ7tHERGRY0GBhYiIiMgx4A69dMMGdwNH4ArRI73O77/D88/D1q2weDGcdpqtmPB6bYjhVk1A+DDigQdKV1J4PPa4iIhIeXOMMeV9D0dddHS0KSwsLO/bEBERkWrODReOdANH6HX694eLL4b16+GWW+zP2dmQkgKJidr2ISIiFZvjOGuNMdEHO08VFiIiIiLHiMdzdDZwBF7nlltg924YPRr69LFhhddrh2v2769tHyIiUnUosBARERE5RkKHXobOojiU60ycCP36wTPP2KBi3jw7tyIlxVZfJCXBv/995O8lIiJSUSiwEBERETkG3DaOwKGXgbMoyhI6ZNPrheuvh9NPh7vvhoUL4Y477HNu1cV119kKi0N9LxERkYpMgYWIiIjIMVBQEDxHItINHIFDNn/6Ce6/H4qL4cknoWtX/3Vyc/3VG7Nm2QqLQ30vERGRikxDN0VEREQqmPx82/bRrh188AHMnBk8kyKwesPjKf1YRESkItPQTREREZEKLrT9A+D//T9bNTFgAKxaBSNHlg4hDrd6Q0REpDJRYCEiIiJSTgLbP3bsgJtvhnvvhb597ayKsgZoPvBA6RDD47HHRUREqoqa5X0DIiIiItWVx2NnUVx/PVx4IWzaZIdmugM0PR77pXYPERGpjlRhISIiIlJO3nkHXnsN4uJg5Urb/lFcrHYPERERUIWFiIiIyHH3ww9260fTpra6YvBgf/tHuEoKt9JCRESkOlGFhYiIiMgRCjc80+u1xwPPWbLEDtXMzoZ77oGff7bzKvLybCtIXp5/poWIiEh1p8BCRERE5AgFDs8E/5rRmBj/OX/4A8TGwv79MG4cvP++rapITVX7h4iISDhqCRERERE5Qm7QEB8PI0YEt3Zs3Qr/+AdER9vNH4MGwRdf2HMWLFD7h4iISFkUWIiIiIgcBR6PDSvS0mzlxGWX2TYQY2DsWKhd254XeI6CCRERkbIpsBARERE5CrxeWzUxZgw89RR8+CGMHw/Nm5c+xx2wqWoKERGRsmmGhYiIiMgRcmdWpKfDTz/BI49Afj4UFZU+RwM2RUREIqPAQkRERI6JSDZnVBVLl8K119qBmllZkJhYenhmQUHwylIN2BQRETkwxxhT3vdw1EVHR5vCwsLyvg0REZFqLbCiwOMp/bgqKC6GF16Ar7+2a0rr1y/vOxIREan4HMdZa4yJPth5mmEhIiIix8SBNmdUdm6VyLZt8Je/QNu2NpApKIAHHijfexMREakq1BIiIiIix0zg5owRI6pGWLFxI7z1FowbB9df7w8r4uMhJqa8705ERKTqUIWFiIiIHDNVaSvGd9/B00/D6afDtGmwYkXVrB4RERGpKBRYiIiIyBHLyLDVBYG/sGdnQ0oKzJ/vDyoq4wyLvXvhuefgxx/h3nv9cyoCq0eSkyvXZxIREakM1BIiIiIiRywmJnhFp9drf4lPTa04WzEOdWuJMTBnDlx9NdStCw8/7A8rvF4YPjy4ekTrSUVERI4uVViIiIjIEQs3YHPBgtJVB+XZEuKGKuG2lrjcSpGoKHj5ZYiNhb59YeRIaNrU/7q+fcFxbKBRmatHREREKjJVWIiIiMhRUdEHbAaGKikp4QOGli2hVy87oyIrC2rUgPR0WykS+LqEBH9YEXjt8qoeERERqYpUYSEiIiJHRWUYsBk6d8INGC67DCZOhN9+gzFj4LHHoFat4GGaO3b4X5eaGv7aFe3zioiIVGaqsBAREZEjFthekZrqr2SoaHMdQkOVGjXsatJbb4UBA6BjR3jySejfP7hSJPR1Fe1ziYiIVEXHLLBwHOdFx3G+cRxnfcCx+o7j/NdxnI9LvtcrOe44jvO04zibHcdZ5zjOxQGvubnk/I8dx7n5WN2viIiIHL6CguD2iorYIhEaqtx/vw0g/vIXWLIEXnzRPp+UBP/+tz+cyM6uHGGMiIhIVeMYY47NhR2nC7ALmGyMaVtyLAP4wRjzuOM4fwPqGWMedBynJ/BXoCdwKTDBGHOp4zj1gUIgGjDAWqCDMebHA713dHS0KSwsPCafS0RERCond6Bm/fp2oOZVV0Ht2lBYCLt22YqKIUNsWBE4mLN3b/tcYqL/Wl6vDWMeeKD8Po+IiEhl5TjOWmNM9MHOO2YzLIwxyxzHaR5yuA/QteTnl4GlwIMlxycbm5686ThOlOM4Z5Sc+19jzA8AjuP8F7gWmHas7ltERESqphtugGefhXPOseFFzZL/CnIcWzGRnGwHbaalBVeKLFhQulJE8ypERESOveM9dLOxMearkp+/BhqX/HwW8HnAeV+UHCvruIiIiEhEdu60QUXNmvDQQ3DKKf7nAttEAteTtm8fHFoonBARETn+ym1LiDHGOI5z1PpRHMcZBgwDaNq06dG6rIiIiFRAbntHYJAQ2qaRng7ffAMnnwwjR8IZZ5Q+50CzNxRSiIiIlK/jvSVke0mrByXfvyk5/iXQJOC8s0uOlXW8FGPM88aYaGNMdKNGjY76jYuIiEjFERMTPPjSrZSIiQFjYPZseOcd+Ne/oFs3f1jhnuN64IHSwYTHo9kUIiIiFcHxDizmAe6mj5uB1wKODy3ZFnIZsLOkdeQ/QA/HceqVbBTpUXJMREREqomMjPAbOfr3twFESoq/reMPf4B774V69ezj2bNLn6PKCRERkcrhWK41nQasBs53HOcLx3FuAx4HujuO8zFwdcljgEXAp8Bm4AXgToCSYZtpQEHJV6o7gFNERESqnnDhRM2aEBtbupoiIQFGjLBDMgcMsMMxv/gCnnwyuMXDPWfECIUVIiIilckxW2tanrTWVEREpHIKHYLpPk5KsjMpRoyAnBz7PNigolUrWLfOVlN07x7+eoGvU2ghIiJSviJda3q8W0JEREREyuQOvQxt40hMDK6U2LkTeveGQYNg8WK7snTgwODqjOxsW5mRlwepqf7rhmsvERERkYpHgYWIiIhUKOHaOLxeWyHx4IOQlQXjxsGrr9pjJ59s20McB3Jz7TW8XkhOtkFFuA0gIiIiUvGV21pTERERqV4iWUXqHsvJsYFDTg5ERcFjj8HQoVCjBvzzn/DXv0Lduv7XeDwwZ46toGjc2L5uwYLwG0DUEiIiIlI5KLAQERGR48JdRRo6n8KdRwGlZ1hceSX07AkdO8Jtt0GbNva8xo1t0BEYPgRWZiQnK5gQERGp7BRYiIiIyHEROJ+irCGYBQX2WNeudjbFokWQmQm7d/vDCvdaoYFEaGWGqilEREQqNwUWIiIictwcrArigQdg5Uo7ZLNbN7ui1HEOft3QygyPJ/ixiIiIVD4KLEREROS4Ca2C2L7dDsz0eODtt+GVV+DUU23LR+/ekV/XrcwIN2BTgYWIiEjl5Bhjyvsejrro6GhTWFhY3rchIiIiAUKrILxe6NsX9u+3cyp69oSzzoLBg1UZISIiUpU5jrPWGBN9sPO01lRERESOi9AqiGbNbEhx0UXwxhvwyScKK0RERMRPLSEiIiJyXLirS7/80raDNGpkV5TWrg0pKdruISIiIsEUWIiIiMhx8e23MHEinHSSDS/q1LHHtd1DREREwlFgISIiIsfUjh3w3HNQXAx33QUNGvif03YPERERKYsCCxERETkmfvoJJk2CXbvgjjvgjDNKn6PtHiIiIlIWbQkRERGRo+rnn21Q8fPPMGyY3fwhIiIi4op0S4gqLEREROSQZGRATExwBYTXCytWwMkn2xaQ22+HJk3K7x5FRESk8tNaUxERETkkMTF2zoTXax8vWgSxsfDhhzBwIKSmKqwQERGRI6fAQkRERA6JO2ciLg6uucaGFC+8AK+8Ak2blvfdiYiIVC0ZKzPwFnmDjnmLvGSszCinOzp+FFiIiIjIIfn1V3j/fbjgAli8GEaPhsGDy/uuREREqqaYM2OInxnvCy28RV7iZ8YTc2ZMOd/ZsafAQkRERA4oI8O2f+zeDc88A2lp8PXX8O67kJwMOTn+9hARERE5ujwtPOQNzCN+Zjwp3hR6T+tNUqckPC38w6SqasWFAgsRERHxccOJQL//DtdeC7fdZr83agSPP25nVaSm2vaQwJkWIiIicnjKav8o2FbAiOgRpC1LY0CrAaSvSK8WFRcKLERERMQncKDmTz/BiBG2omL0aPjvf2HyZFtVkZkJiYn2Ne5Mi4KC8r13ERGRyiRcOFGzRk1ip8WWCiNq1qhJTmEOyV2S+ffmf5PUKclXcRE/M568gXlBFRdVhdaaioiIiI/HA//8J/TuDR06wPr1sHChPX7CCTa8SE72hxWBr/NUvf9OEhEROSwZKzOIOTOmVNtGwbYCHrjiAcA/m8ING7xFXtJXpJPqSSV+ZjwjokeQU5hDUqck0lekkzcwj8ubXM55Dc5j5KKRtD2tLWnL0kjuklwlwwpQhYWIiIiU+O47SE+Hd96BYcNg+XK46y4bRHi9dlaFZlaIiEh1F64yYvj84QyfP9z3OObMGPpN7+c75i3y0ntab2rW8NcMeFp4SOqUROy0WFK8KcTNiCOnZw5XNLmCK5tdSdqyNFo1bMWijxfR8489WbplKVmrs9hv9nPjn27kna/eIalTEjmFOaXup6pQhYWIiEg1kZFhWz4CKyG8XsjPhz/8ARzHBhUbNti2EDeciIqyQUZenr+SIj7e/1hERKSqCK2MyFiZQc0aNSneX+yrjHDbNuYPnu+rjMjdkIuDQ0LbBN9rDYbpG6bT+JTG5BTm8PdOfydtWRq/Ff9GvZPqsfrz1czYOINz659L2rI0ujTtwne7v+PjHz7mjaI3uP/y+3nxnReZETejVKXGqI2jWHjDQjwtPHRv2b3KtoWowkJERKSaCJxPATBjBvTqZTd+3HknjBnjDyvy8vwDNZOTISnJH05oZoWIiFRGZQ20DNyuEbpCtGaNmoxePNpXGRHathE4Q+KZns/Qd3pf+uT2ofe03vQ9vy/tGrfzVUqc9H8ncc+l9zB+5Xg+/O5DFn68kHFXjWPbrm0kd0lm43cb+XXfr2S/mc3s+NlkdM9gRtyMoPsBKNhWEBROuFtECrZVvf9jVoWFiIhIFRSumgKgf38YMADatIG337bhxA03QIMG9vmCAhtOFBT4qykWLCgdTmhmhYiIVDahMyOGzx9O7oZc5g6aG3Re/wv6B82QyOiewbhl49jwzQZmbJzBTe1uYueenbRq2Iq0ZWl0btqZtV+t5ew6Z9Pn/D5MWTeFpE5JvsqH5C7J5BTmMPb0sXhaeNhv9pO2LI0h7Yb4ZlN4WnjwNPfQe1pv0jxpYcMI95hb6RHI08JT5aorQBUWIiIiVVJoNYXXa8OKn3+2z61YAaNGwc03B58XE2PbP2ICNqN5PPBA6f82EhERqbDCVVOAP4xI8aaQuyEXDOzau4t129eRvjyd2Gmx7Cne4wsjWjVsxS97f6Hj2R158d0XueFPN5DeLZ2uzbuy6btNJHdJZtN3m+h4dkea1GnCvzf/m+QuyTxb8Cz9pvcjb2AeqZ5U8gbmET8znuzV2b5tH7M2zSKpU1JQOLFg8AKK9xcH3bOnhSdsSFEdKLAQERGpAjIyggdhejy2UiI2Fm67zbZ+3HqrDSjefts/nwJse0d8PKSkaDaFiIiUr0jaNg5l6OVtr93G5h82k706m+tzr6d4f7EvjLiw8YX0vaAvg2cNJvV/qYxfOZ5/9fkXQy8cGhRGnHriqby17S1fyPDPd/7pq9Rww4i+0/sGBRQJbRIwGN/9uAM2U7wpvnMWDF5A+or0oM9SncOJcNQSIiIiUgW4FRVu2JCfD2PHQtOm8OKL8NBD0K1b8DmBwzNHjPCvLFVYISIix0O41Z+hAy3DtW2457yW8BqtGrVizqY5TFk3BWMMe4r30DyqOVt2bGF38W5eff9Vvt/9Pd4tXp7r9RwNazfkpjk3+ds0uo6lWVQz33rQBrUbBLWNRNWKYvTi0WT2yCSxY2KZbRsJbRJ8PwNMip1EQtuEoFaO4v3Fvs/lnhva7iHBHGPMwc+qZKKjo01hYWF534aIiMhx5fVCXBxcdRXMnw833ghz59qBmjk5tiUkIaH0lpDcXJg924YWOTmqsBARkSMXLoxwKyAmxU4CbOVEv+n9GNRmEJNiJ+Et8hI/M56kTkk8tvwxbrnoFnIKczDGcHuH24mqFUXRj0XM2DiDTk07sfLzlXRt1pUVn6/gyR5P0ujkRtw671bf7Im8gXl4t3h9YYSnuScojPAWeek7vS8ODndfejc5hTn0v6B/0KaPcFtCvEVeCrYVqBLiCDiOs9YYE32w81RhISIiUgXs2wdffAHnnmu3f9x0E7z2mv05sJoiIaH0a2fP1spSERE5fJFUSoSu/uzYpCNf/vQl+/bvY8q6KXz0/Ues+XINca3j2LlnJ60btSZzdSYDWw3E08JDsjeZO6PvZNHmRb51nineFF8YcevFtwIwInqE7xjgmxeRU5jD9l3bS63+dHAY1GYQqZ5UX6CR0Nb/f5bVacBlRaQZFiIiIpVM4LyK3bttVcTQobaaYvNm29Yxe3Zkq0gLCoLDCa0sFRGpWCKZ6VDe7x+6CnTJJ0sYt2wct7W/jT65feg+pTu9pvai7/l96XN+H3pN7UXPV3syYtEIHvU8ym3tb2PpZ0sZffloXu73ctBAy6WfLaVVw1aMjBnJuOXjGBE9wheABIYR3iJv0LEJayaUGno5+4PZQZ+jYFsBcwbN8VV8VOX1oJWVKixEREQqmZgYGDjQfjVsCOefD4sWgePAnDnBlRLt2weHEaFVE+G2f2hlqYhIxRG6itNtm8gbmHfA14VWPYRrbQht0YDS7Q6h75//aT69p/Xmzpg7WfDRArbu3Mo3v3xD+9Pbc80r13DZ2Zex9qu13NHhDq5ueTW//f4bk9ZOIrlLMqmeVICgmREXnn4hj6541Bc8RNWKKrXq023biOScOYPm4GnhYfuu7XYLSInqvh60slKFhYiISAUXWFGxZQssXQqXXgpTpsAJJ9j1pAkJ/rACVCkhIlJVuL9ou6s4A8MDV7gqCLclwz1es0ZNRi8eTc0a9m/WbovG9A3Tfed4i7z0mtqLH3f/yBufvsG/3v0XKz9f6QsjurzUhd7TetPjnB48v/Z5Pt/5OQNaDaBz08688/U7JLRNYPnW5YzqOIqsa7KoVbMWszbNOqQqiGRvctCqTwhu2wh3jjv0clCbQUFDL+cOmhtULaENHJWPKixEREQquJgYOzDz2mvh8svhkktg4kRbYeFu9khNLf06VUqIiFQNnhaeoNkM7i/h7i/n7grPwOGV6SvSSfWkEj8z3jeEMqN7BuOWjWP9N+uZuXEmN/zpBnbv202vqb2IPjOawm2FeJp7eKbgGRqf3Jg+F/Th4+8/ZsKaCSS0TWDKuim+Sgm30uOrXV+RU5hDUqck0lekH3EVxILBC4JCBrdtIzCcCD0HgqtEAq+naonKTYGFiIhIBWUMLF5sv0aMgOeft0M1U1PtfIr0dBtW5OQonBARKU+RbMSAyLZLhLtW9upssldn+8KApE5JpSot9pv9TFs/DYMhd30ut150Kz/99hOtGrYibVkanZt25td9v3J5k8t56d2XGN5hOBndM6hzYp2gFo3AMOKHPT+EDSM8zT1BIcqQdkNKhROHu/ozNGRQ20b1ppYQERGRchTY7uE+fuIJ2+IxerSdS9GrF0RF2fWkaWlw3XU2rMjLs+FFXp6dV+H1lv0+IiJy7IQOnQzXbjF8/nD6Tu9LzJkxvtcNnz/cF2y4Qls5sldnM3rxaJK7JHNTu5v42xV/4+GlDxN9ZjS9pvaiy0td6DW1F/0u6EfHJh154e0XiG8TT1LnJDo37ewbXrnpu02c8odTWPPlGpK7JDNr0yzWblsbdnhlYBhx3R+v84URbktG/Mx4sldn+143a9OsUi0aCwYvoHh/cdBnmxQ7qVQlhNo05EBUYSEiIlKOYmL8a0Sjo2H1arvt4777ICvLhhDx8baiIifHVlRkZdngIty8ClVZiIgce6FVEJ4WHpI6JRE7LZbEjonkFOYwd9BcAF9LhrvS0xW45jOudRwXNLqAuR/M5ZGlj+Bp7vG1aaz+YjVXt7ya/WY/b335FjFnxTCp1yS27NxCzJkxvsoIdyWnGzy0btQ6qOohqlYUoxePJrNHJokdE8O2aLjXSOqU5AsjslZnlaqUSOqURIo3xbey1H1d+9Pbl1kpIXI4FFiIiIiUI48Hnn0WeveGDh1g/XobSKSnwymn2JDCbf9w149GugFERESOjXCbO9JXpNO/VX9/gFDyy/odHe4gbVkat198O83qNiN2WiwdzuhAwbYC4lrHAdBneh88zT0s37qcCddOYGDrgTyx6omgNo1QbtuGO7zy6TVPBwUPoS0ZxfuLyeyR6at6CNeiEWkYUby/2Pe8+7rQDRwiR4MCCxERkeMkI8NWVLjBQmGhDSd+/tm2e2Rm2gqKxETYscM/ULO42B9WgCoqRESOlUhnUQD0v6A/8TPj+Uv7vzBp7STi28Tz6vuvcmWzK8lclclnOz4DYMbGGfQ4pwe563PJuDqD4R2Gk/1mdplrPm9pf0upNg13ZoQrcLVppMMrw7VdhBtUGUkYobkScrw4xpjyvoejLjo62hQWFpb3bYiIiATxeiEuDu6+G3buhJNOgueeg7//3VZQjBgRXFHhPg4MK0RE5OgJDSi8Rd6gbRtLPllCv7x+GGO477L7qHNiHdZ/s54ZG2cQ1zqOoh1FLN+6nCuaXMH6b9aT0yuHAa0HsHLrylLtFt4ir+/Y3ZfeTU5hDnkD8wCCNnm4Ay4DqzdCB2yGC1YiGegpUlE4jrPWGBN9sPNUYSEiInIMhFZT/PwzzJkDZ50F2dnw178GhxVuKBEVZYdtZmbaSgu3/UOhhYhI2SKpjMhYmUHNGjUp3l/MA1c8gDGG34p/o+fUnjzU+SHq1arHW1++xe7i3bz83sts+m4Ta79ayx0d7qDxyY1JX5nOsIuHsWjzIhbesBDA15LhznkY/KfBQPh2CwAHh0FtBpHqSS1zhkS47RqqcJDqSoGFiIjIURAaUMTEQL9+0LMnXHABfPIJzJ8Ps2bZSouy2j2Ki21YUVwyWF3tHyJSlUVSKRB6TmjwAP7NGm4rg7fIa1d8GsO59c+lfu36eIu8vP7J63Rv2Z1f9v7Clh1bmLVpFgltEshancWtF93Kwo8X8vqNr+Pd4i01P2LXvl2+Y0BQ1UO4OQ+h7RYF2wp8wQSUPUMitJXDPa4wQqojBRYiIiJHQeC2D48HNm6E3bttVcVf/wqLFtmwAvzbPsK1ezwQppJXAzVFpCoIF06EBg3D5w8nd0Oub8NGuHNq1qjJqMWjGNNlDCu3ruT1za+T/WY2VzS5wrdZo3BbITe1u4nTap/GuOXjGHrhUAq2FZDVI4v0FelcdvZlLNq8yHfNJt4mQWFE6PyI0GPbd20PatGIZOhkpDMkFE6I+CmwEBEROQo8Hpg6Ffr0gTZtYMMGWLgQli3zV1NAcKihdg8RqYwinZ8Qel7MmTFB8yHcR9MlHwAAIABJREFUzRqpntSg1Z8Y2LlnJ+989Q4LP17I4yse5/ImlweFEdeccw1PvfkUn/7wKYs2L2LGwBn0PK8nKd6UUpURNWrU8B1L7JjIjj07gjZ5BA64DLdto6zVnwltE4L+XRQ0iBx9CixEREQOUWj7xzff2EDio4/sUM0XX7SPTzghuJpi+3Zt+xCRyi/cSk/38YHOAzAYctfnckKNE3j1/VcZfvFwftn7C60atiJtWRqdm3amRVQLbppzEz3P7cl/P/0vU/pNoe8FfXl46cNBYURgONHzvJ5hN2tAcGVEVK2oUo8DB1yG27YRrm1DKzxFjg8FFiIiIofIbf8YNw62bIEffoCZM+Ghh+wAzeRkmDABnn7atoQEVlMkBP9BTu0eIlLpuL+wB2626H9Bf8CuxNz28zY+3/k5bxS9QcuolkGVEXGt4/ji5y/IKczh5gtvZuQlI/no+494+q2nfSHC2K5jg9Z89mvVr1QYcbDgIVxlRFStKEYvHk1mj0wSOyaGHXA5KXYSCW0TgsIItW2IlB8FFiIiUm2FVkqAHYhZUBA8SyLwvH37bKVE27Zwzz0wahTMnu0PK9wKiu3bIdf/RzpVU4hIuTucTRqB5zzX+zm+3/09W3duZeXWldSvVd9XFbGneA+9pvZiUJtBXNH0Cn7Y/QPPFjzLq/1e5c0v3/S3YJS0U7hBQ7vG7coMGsoKIyIJHsJVRhTvLyazRybF+4t9xzXgUqRiU2AhIiLVVuigTK/X/zj0vIED7VeDBtCsGaxfb8997LHw2z4mTbLVFIEBhaopROR4iWTApbfIS+6GXBwcEtomcMlZl/D97u/JWJlBfOt40v6XxuYfNvvO2VO8h+gzo9mxZwfjV46nhlODMZ3H8Nza5xjbdSx/vujPxM+Mp0ndJuQU5jA7fjbAAedDhAYNUHr1Z+g5kQYPoZURWgUqUvkosBARkWrLrXqIj4cRI8Jv7XjrLfjPf2xYMXMmjBwJY8ZAUpK//SPc69zrK6AQkbJEOrwykteFVkqEDrhc8skSxi0bx58v+jN9cvsQc1YMqz9fTVzrOAB6Te1FxyYdKfiygJExI5n6/lT+WP+PLNq8iNdvfB2wazybRTVjwpoJ1KxR0xc8XNXiKt+sihHRI8pc/RluPkRo0BBu9WfoOQoeRKoPBRYiIlKteTw2rHA3eRQUwN698O238O67cMkl0K0bvPOODSvS0mDIkOD2D237EJHDEW54pVtNEOhgYUT+p/lMXT8VDJxd52yiakVRuK2Q3cW7efm9l9n03SbWfrWWO6PvpMc5Pdhv9vuqHtxNGoEzI1I9qdQ/qX7QJg3AF0Z0a9GNhzo/VGoIZe76XGZ/MLvM1Z/h5kOEBg0KI0QkkAILERGp1rxe/yaPZ56BSy+FRx6xAzMzM/1tIklJ/vOysmxwoW0fInIkwg2vTPOkkb4infant/eFGNPWT8MYwzn1z6HBSQ1Y+fnKoDCicFsht7W/jcYnNybrzSxua38bCz9eyOs3vo53izcoiPAWeZmxccYhbdIId044sz+YHTSLQqs/ReRIKbAQEZFqy+u1a0jvvRd27oShQ2HKFLv9IykJtm61IYXb/hFaUdG+veZTiFQHkbRuhJ5zoOGVgbMVivcXc17980hblkbfC/qy7/d99Pxjz6DNGkPaDaHRyY14bPlj3Hzhzcz7cF7YMAJg7/69QS0ZR2OTRug5bhgRWD1RsK0g6LFWf4rI0aDAQkREqoRINn4EnvP117aCol07+OILG0w4DvTpY18T2CYSOlBTFRUi1Uto68bw+cPJ3ZDL3EFzfeeEDrSsWaMmoxaPYmzXsazdtpZFHy/i5fdeBmBP8R6aRzVny44tTN8wnRpODW78040s/Hght7e/nQc7PViqRQOghlOjzDAitAoikgGXkW7SCD0nXBihVg4RORYcY0x538NRFx0dbQoLC8v7NkRE5DgK3PARuvHDDRXy86F/f7juOujQAVq0gDvuKD17wn1tWYM4RaR8He6wykiuE64Kwlvk9c1nGBE9gglrJuDgMLX/VFrUa8H8D+eTtjyNK5pcwbLPlvkqIzo17cSqz1fR69xeLP50MS9d/xJ1TqzDoFmDgq7jhgreIi/xM+NJ6pRE+op0X5tI3kC7ushtHQn3utAqiMBQxf18h/NvJCJyLDiOs9YYE33QE40xVe6rQ4cORkREqp/8fGMaNjQmOdl+z8+3x3fsMObZZ40ZPdqYRx81pkGD0ueEXsM9HvpYRMpf/qf5pmFGQ5P/aX7Yx8YYM37F+KDHxhgzbN4wM2zesKDr1E2v6zuW/2m+qZNex9RNr2sWb15stvy4xTy1+ilzymOnmNvn3W46v9jZ8Aim84udzdDZQ03tR2ubfrn9TN30uib3/Vyz7/d9Jjk/2fAIJjk/2RhjSj0OPNbt5W6l7jFrVZY5+dGTgz6be0/usWHzhpk66XWCXhv62dzXjl8x/vD+kUVEjiGg0ETwu71aQkREpMoI3Phx1VWwaRMsWQK1asGNN8Jnn9k2jjvv9Ld7hFZOFBSo/UOqt2NZvXC0rgPQ/4L+QcMq+1/QP+j50E0a3iIvuRtycXAY1GYQbRu35aPvP2Lv73uZ/N5k3/BKd81n3+l96daiG//77H88c90znHbyaQydO9TXgjG269igto1BbQfhLfIe8fDK4v3FvrYSCN+SEW7bRmBFiEstGSJS6UWSalS2L1VYiIhUT/n5xtSvb8x11xnzhz8YU7u2Mf/5j/+5hg2NycoKX4UhIlZotUK4v+ZH8pf7cFUQtR+tbbJWZZU6L/BaoZUR4aog3OsGVi8EHv/5t5/Ni2+/aGo/WtucNO4kc+VLV5qTxp1khs4eaobOHmpOGneSuXbKtebUx041kwommVH/GVVmFUTotd17cKsekvOTTcOMhiZrVVbQOVmrsozziOP7vOEqJcJVhoiIVAdU5AoLx3G2AD8DvwPFxphox3HqA9OB5sAWIN4Y86PjOA4wAegJ/Ar82Rjzdnnct4iIVEzG2JWkDz4IgwfDQw/Zaoq+fe0sirvvPvC2D82oEPELXbXpViW4vEVe3/DGQKHVE5Gs7IxkeCWAwTB9w3Qan9KYiQUT+cd1/2Dd9nU8+eaTXNX8KjJXZfLZjs982zUub3I5b335Fo93e5zNP2zm6beeDhpeGVgZcW6Dc3nI+9ABqyC279oetAED8FVqpHpSww60PNzhlSIi4lcuQzdLAotoY8x3AccygB+MMY87jvM3oJ4x5kHHcXoCf8UGFpcCE4wxlx7o+hq6KSJSdRxo+8dtt8HUqXbLx9dfw5AhcPXVwec9+ii88YZt/zjllINvEhERK8Wb4vul3l1j6QYP7lDIcFszQgc87tq7K2jbhTtYMtzwyPxP84mbGcfQdkP55zv/pGOTjiz/bDlxreMo2lHE8q3L6dqsKzFnxTBp7ST+cd0/GNh6IGu+WOPb4hG46jP0vg9neKV7v4GBxdFqdxERqa4iHbpZkWZY9AG6lvz8MrAUeLDk+OSSspE3HceJchznDGPMV+VylyIiclzFxARXQeTnQ8+ecMUVsH8/3HADNG3qDx4CAwuA996zYUVZ2z7cSguR6iDSX7RDZzF4mnsYET3CFwQkdkyk/entD1iF4W67CLzOpWddSot6Lejesjtpy9K4stmVNKvbjF5Te/k2a9x+8e1c1eIqftn3Cy+8/QJjOo/hqhZXET8z3ned8xqcFxSOuJUK7iaPstZ6hoYR23dtJ3dDru++tcJTRKSCiaRv5Gh/AUXA28BaYFjJsR0BzzvuY2AB0CnguTew1RmaYSEiUk24syl69DDmpJOMue02u+njQJs8tO1DpLRI5lMcaEuFO6/BfS5wzsN/Pv6Pqfd4PTN09lBzymOnmJ6v9PTNjUjJT/Ft1bhp9k2mbnpdc8+/7zENxjcoNYsi8D6T85MjnvsQyWfTJg0RkYqBijzDoiSA+NJxnNOA/zqO80Hgk8YY4zjOIfWqOI4zDBgG0LRp06N3pyIiUm727YNFi2DVKujQARYvttUSqal260d8vN0KEq56Qts+pLqLZLtGuMqIZG9y0CwGAAzEnh/L9edfzwnOCcROi+XyJpezYusKOjftTOaqTL5o+wWdmnZi8rrJ3Bl9J2ecegajLx8ddJ0LT7+QFG+Kbz5Fn/P7+KoeAjdrBLabhKuCCDf3oWBbQVDbhjZpiIhUfuUywyLoBhznEWAXcDvQ1RjzleM4ZwBLjTHnO44zqeTnaSXnf+ieV9Y1NcNCRKTyysiAhg3h889tYNGzJ6xeDQ8/DImJweFESop/PWlqannfuUiwY7nWc/j84YD/F/CMlRnUrFGT4v3Fvmtnr84OCgcCZzGEznkYOGMgca3jmLZ+Gn9p/xfqnFiH/WY/ACs/X8lZp57FpWdfSpM6TWhatynzP5pP+vJ0FtywoNTsh7svvds3LyI0CAj9LN4ib6nVo+7wysSOiUf07yYiIhVXhZ1h4TjOyUANY8zPJT/3AFKBecDNwOMl318reck84C7HcXKxQzd3HiisEBGRyiNwoOaOHTB9Orz+OqxcCXPm2LAiOxvuvx8yM21g4W72SEqy4YU7n0KzKMpXdRtCGPp5wwUGodsuAgODQxFzZkzQ0EdvkddXGZHQNgFPCw81a9Rk9OLRZPbIBOy/ffqKdFI9qcTNiGNw28FMWTeFO2PuZOr7U3n1/Vd9lRGf7fiMi0+/mElrJ3HLRbeQ2DGR0085nRNqnFDmPf3nk//4wgpX6NaM0EGVUHr2Q8G2At88CbDVDgsGL6BgW0HQeaqCEBGppiLpGzmaX0BL4L2Srw3AQyXHG2DnU3wMLAHqG/88i2eBT4D3Ocj8CqMZFiIiFdb48cEzJJYsMebkk4256CJjHnvMmClT7JyJrCz7PTnZmNq17eNAWVn2dZpPUXGEzg8oa85AVRH6+bJWZRnnEcdkrcoKej5rVZZvFkPtR2v7nneFm6kQ7pg7VyJwhkT+p/mmwfgG5r7X7zN10+uam+fcbE5+9GTT+cXOQbMjur7U1fAI5qZZN5nJ7072zY1w77Os+RSHYvyK8WFnSmg2hIiIhENFnWFhjPkUuDDM8e+BbmGOG2Dkcbg1ERE5xtyNHxMmwNatsG4dGAOffgq7d8N99/nbPXbs8Ld7JCYGX6e4GObP13yKisSdKxC6QrKq/lU83OfN7JFJ+op0duzZEfT5d+zZQdqyNIa0G0L6inTan96+zEqJ0GMdzuzAzI0zGfu/sbQ9rS1py9Lo3LQzS7csBaBNozY8+eaTDGoziPsuu49GtRuRuTozaIXoxMKJvvkQtf+vNjPiZhxyZcTBaGuGiIgcCxVpramIiFQhge0eADt32gGaZ50Fw4bZYZn//S8sWGBXkrrhhMdjHx+o3eOBMB0Gagkpf54Wwasvq8ovqwdqdwld9emGE+7nD10PmtQpyRdyTCyYyMSeE/n2l2+5Pvd6Ys6M4c0v3iSudRwAvab24oqmV7DmizXcctEtTFk3hYc6P8SktZMY23UsQFAYcclZl/Cv9/5V5vBKN4xIaJvg+xzhWjLCDbQUEREpDwosRETkmIiJgbg4GDXKhhXffw+zZtmvwIACgsOJqChIT/dXWrgzK0K3gEjFE/rLuad55fsLe7hwoqxZFEmdkoI+b1StKN/jiQUTqeHU4Kk3n+K+y+6jzol1uO6P1zEmfwzn1j+XtGVpdG3elX3799Hu9HYMvXAoEwsm+iojAJpFNfNVZkxdP5VZ8bPwtPDQrUU334BLN2yIqhXlm2GR2DERT3OPb3jlgcIIVUaIiEhFpsBCRESOKmPg7bdh6VK49loYPx7++leYO9eGFeAPKCZMgKeftgM23XCid28bZqjdo3IJHCgZ+Nf88mwLiWQwZui2jZgzY0ptrXCHVwa2f9x32X2kLUvjwSsepF6telx8xsWMWjyK7i274+DQ69xePLb8MYZeOJR+rfrRpE4T7q11LxedfhEp3hRfyNGsbjMA8jbkBQU9gC/8yFqdVSp4SGiT4PsZoHh/MZk9MineX+w7ruGVIiJS2SmwEBGRo+Lvf4cff4S6deHii+Fvf4M334Svv4Zx4/zVFIHVEtu3Q26u/xoej20RKQj+HUvtHpVAwbaCoHCiIrQWhG7XCLdJI3SGBMB+s59p66exu3g3cz6Yw6A2g9i5ZyetGrbyzZBY9fkq7r7kbro270rTuk35cc+PXHPONUFhyJ8v+jMF2wpo17id7/3SV6T7KjU8zT2lKiXKOhY/M943+wL8AYtLlRIiIlIVOXamZdUSHR1tCgsLy/s2RESqvJ9/htmzYeNG+PVXmDoVZs70z6Ho2xccB+6+21ZV9O8PCQnB4YPXawOKcHMppGI63itMw71faGVEuOoJb5GX3PW5zP5gtq8y4sErHiR9RTp9z+/LjI0zuKndTezau4uZG2cSfWY0hdsKGdx2MN/9+h3zPprHyJiRZPbIZPXnq494oGgkn6OsY1V5RayIiFQ/juOsNcZEH+w8VViIiMgh+e03OzRz715o0wb69YObb7bBw969toJixAjb7uE4we0e8fE2sAik6onKJ7RyIbAd5EhFOkMitDLCrZ5I86Sx/pv1zP9wPo8uf5QBrQYEVUbs2ruLS8+6lBfffZFhFw/jsW6PUffEujSPau4flllS0eC2aLSs1zLs8MqjsUkjtFKirGOqlhARkepIFRYiIhIkdLtHRgbUqAEffQQNG0LNmnbl6D//ads33GoKt9XDHajZrRs89JCqKaoqN6Q4UMVBJJUYoed4i7ylZki4Ay4fW/4YCW0TmLJuCndG38m3v37L1Pen+iojOjXtxKrPV3HtH69lyadLeCH2BerVqsfg2YN995nUKYn0FelB9w34PsuENROC2jG8RV7f8MrEjollfg4RERGJnCosRETkoELDCbCBRGwszJsHp5wCS5bY9aPDhkFqKixfbsOJtDR/NUVOjg0rIHjjRyhVU1QdkawwDa3EGD5/OLkbcpk7aK7vHLd64rWE12jdqDWbvt3E3t/3Mvm9yWz6bhOF2wqJax3Hzj07ade4Hc8WPMuQdkP4y8V/4aw6Z3HmqWf67iHVk0qKN8X3uGHthkHvH26TRui8iO27tpO7ITfoc2p4pYiISPlQYCEiUo3FxAQPwXSrI7p0sds6evWyGz+ysuyq0caN/eGEx2MrLQLXkwZeS+tIj69INmJEUhUQ6ZyF7NXZZK/OPuAKU3fwZvzMeG656BZeff9VjDHM+3Ae//vsfxT9WMSMjTPo1LQTsdNi8TT3sOLzFfzjun/w4fcf8sSqJ3xBhLfIy8TCib73u+WiW9i6c2uZa0VzCnPYvmt7UOVHuE0aods2JsVOIqFtQtCwUIUTIiIi5UOBhYhINeauDB0wADp0gJUr7YDMpCQbUrhhRGJicDjhhhuB1RTbtweHE1pHenxFshHDbW0IFBpihJtPETovInt1dlClwhVNrmBA3gDGdBlDw9oN+eKnL/it+Dffe7Rq2IonVj3BgFYDuKr5VSQvTebO6DtZtHkRC29YiKeFJ6gyomW9lvztjb8FBRGhMyRCKyPCVU/Ez4wnoa1/aEqkMyQUUIiIiFQMCixERKqpzz6zGz62b4fLLoN//9uGD6mppcOIqKjSj9PTS1dTVNWBmsdzK8bhvldgNYM7nyGzRybpK9LZsWcHOYU5pHnSSF+R7luPGS7E8LTwkNQpidhpsSR2TGRiwUT+X+z/49tfvqVPbh8uO/syvFu8XN3yanbu2cnD3oc5seaJDO8wnA+/+5A+V/Th7Dpnc2LNE333HlgZMTJmJCNjRga1kniLvL7KiAlrJvD0mqeDVnq69xhY8RBaGRGueqK816qKiIjIkVFgISJSBYSbRTHcVvEzKeAPyDfeCEVFtuWjWTMYPNiuIl22rOwwIioKRo+GzExbaeHx2HaRtLTqU01xLLdiRPJeoaHCgdo9AudKJHZMZMeeHUGP25/e3hdqTCyYyN87/Z20ZWn8VvwbUbWiePOLN5mxcQbn1j+XtGVpdGnWhe93f0/zes254U83MGntJF+bxsEE/juFVkaUVT0R6QyJ0MqIcGGOKiVEREQqtxrlfQMiInLk3FkUXq997PVCbi5Mn26/JkyAG26wFRXr18M119hhmVOn2jAiNdV+5eXZ4CIpyR88FBfbsKLY/uEaj8duB3Efuzyeqrv9I7B6IcWbclgrLY/kvdzKCG+R/R/YbfeoWcP+3cENBmrWqBk0w2H8ivE889YzDGk3hCfffJLbXruNpVuW+tZ8tm7Umtr/V5t7Lr2H8SvH89H3H7Hw44WMu2oc23ZtI7lLMhu/3cj5Dc7npJonMWvTLN+13Xs5kIJtBaX+nRwcBrUZRKonlbyBeSR7k0nqlBQ0Q2LuoLlBAYWnhUfbOERERKojY0yV++rQoYMREalu8vONadjQmORkY+rVM+auu4wZPNiYk0825t577XP5+cHn1a5tTFZW6euMH18+n6GiS85PNjyCSc5PPui541eMN/mf5gcdy/8034xfMT6i87q93C3ovfI/zTcNMxqa5Pxk0zCjoXli5ROm3uP1zC1zbzGnPnaqiZ0aa04ad5IZOnuoSclPMd0ndzc8ghk8c7DxFnnNK++9YhqMb2CyVmUFXcd9b/ezDZk9JOh4/qf5pk56HVM3vW7QscBzIhXpv4mIiIhUbUChieB3e7WEiIhUEc2awcUX21aNa6+1VRJnngkpKcHDMsFWVwQO1AxUVeZOHG2BcxayVmcRVSuKxI6JQc8fbHhluKGX7lrP+YPn+87rk9sHB4dhFw9jwpoJ/PTbT0TVivJVRnRu2plf9v5Cx7M78tK7LzG8w3DOOPUM7rvsvqAtIdf+8VqK9xfTtXlXALb/sp0Ub4rvvdzBlEmdkoI+28HmRRzufAi1bYiIiMihUGAhIlLBlTWfwhi70WPhQrvBY/NmWLHCP4viww/tV+CwTPcaoccUUBxY6CwGdyMFQGLHxIiGVwYOvWzTqA3n1D+H1z54jUf+9widm3Wm19ReRJ8ZzZov1+DgcGv7W+nWohsXnn6hr21i03ebfC0ZfS/oy1vb3vI9Dm29CBcOFO8v9oUVgfcYLsRwB3OCNmmIiIhI+VBgISJSwbnzKfLy4Mor4bnn4OWX7XONGsH998OLL8L48cGDMfv2BceBOXP8oUS4Y+61FVqULXQWg1tZkeJNKbWBo91p7WjVqBVzP5jLI0sf4YKGF/iqInbu2UnPP/akf15/urfsztItS3mu13MMbD2QR5c/StqyNLq16MZDnR8KCgP2FO8JChXKWuF5sLkakYYY2q4hIiIiFYECCxGRCq5zZ9ve0auXbflYt84GDrVq2bDhhBMgK8sfVoANH9wVo4GbPMIdqyrbPSJZBxp6TrhtG8Pn2/UqgVUFMWfGULCtgK7Nu7Jjzw627tzKeQ3Oo0uzLqXCiD7T++Bp7mH51uXcEX0H/3znn74qiLFdx+Jp4aFZVDPf5o4b290Y1G6SU5hT6rOFhgpHc4Wn2jRERESkolJgISJSwWRkQLt2sG8fvPkm1KgBderAZZfZ7R/JyXDddfbcA82imFS6ij/ssarSEhI6M2L4/OHkbshl7qC5vnNC50W42zYye2QC8PrHr/Pq+68CEFUrilNPPJWPv/+YGRtnENc6jkeWPkK9k+rRpE4TvvnlG9Z8uYYxncfw3NrnSoURQ9oN4aV3X2Jm3Mwy50WEW+sZrloiNFRQyCAiIiLVgQILEZFyFDifYvt2uy508WIYM8ZWTaSlwf/+52/lqI6zKMJVToSrggDof0F/4mfGMyJ6BLkbcnFwfM8t+WQJ45aN49b2t9Intw+XnnUpKz9fydUtr2ZM/hjmfjCXtV+t5Z5L7+G02qeRuiyVEdEjWLR5EQtvWFiqcuOOhXf4woirWlwV0fDKcPMi3NkXaskQERERCabAQkTkOAkdnmkMfPstXHMNxMXBJZdAgwbw3nvw+OOQmmqfnzCh6s6iiCSMiDkzhn7T+zGozSAmxU7CW+T1hREJbRPwtPCQ/2k+cTPjGN9tPDt/20nasjS6NO1C86jmvmGWa79ayx0d7qD7Od3Z+/teJq2dRHKXZFI9qaR4U3wtGqmeVAB+2POD71hocBA60yLS4ZXh5kUsGLyAgm0FQddXtYSIiIiIAgsRkeMmJsYGE0lJsHMnfPIJzJtn145OmADnnAPjxvlDhx07bIVFt27w0ENVYxZFaEARSRgBsN/sZ+r7U/l136/M/XAuca3j+H3/774wonBbIbe2v5Uvf/6S1ze/zn2X3cfk9ybzSNdHguZFpHpS8RZ5mbVpVlBLRmCLhqe5fc/QY4ezgSO0UkKtHCIiIiKRU2AhInKMuBUVF10Er78O779vh2aOGWPnTSxebAMLjwf27vXPovB47KyKwHaPUBVxFkUkAy1DZ0iADSOmrZ/Gvv37mLlxJoPbDmZP8Z6gMOLGP93It79+yyvvv8JdMXeRdU0WfzjhD0FhhFvRMGfQHDwtPMSeF0vf6X1xcMqcFxFu24b7Gvc6R7KBQ2GEiIiIyOFTYCEichhC2zsyMqBmTSgutmtG33sPli+34cQtt8Bdd0HjxvDCC7bK4rHHyg4noqIgPd1faVHe7R6RzpAIN9By1OJRpHnSePfrd1n40ULSV6RzRZMrgsKIQW0G8e2v3/LSuy9xR4c7yOiewaknnho2jHCDh/6t+gPBVRDbd20vFSo4OAxqM4hUT2rYeRHhtm0ktEnw/ex+10wJERERkeNPgYWIyGGIiQkOEYqL4cEHbfvGzp02vFi1ys6iSE+3YUVOjm0HSU8/cDjRu7ettjgW7R6Hs/rzQG0b/S7oR8v6LZn3wTzGLhtL56adg8KI7i278/iKx1m3fR2LP1nM5L6T6deqHw8vfbjMMCK+TTzgDyMmrJnA02ueDqp4KKsKIqFtgu9zFWwr8D0P4eeobw01AAAgAElEQVRFhKuKCB3k6b5WYYWIiIjI8aXAQkTkIEKrKcAOzOzaFWJjbcvHO+/AvffClClw+eUwcSLMnBk8i2LIkNLhxDWpGfzl/hg8JRf3eCDtFS9LNhaQiP+X6aPV7nEoqz/nDprL+Q3PZ/0369n7+14mvzeZTd9tonBbIXGt4wAYMGMAPVr2wLvFy/O9n2dA6wGMWzYuaGZE4EDL/q374y3yHlIYsX3XdnI35Pr/LSKsglCLhoiIiEjlpsBCRCREaEAREwP9+kH//vb79Okwezbcdx80bQrZ2bZiIjUVTj217FkU7prSwMqJx3fEkLIunrgiGyB4i7ykb44n74Y8//1E0JIRbl7EgVZ/xs2I488X/ZlX338VYwxzP5jL/z77H0U/FjFj4ww6Ne1En+l98DT3sHzrcp7t+SwffPcBGasygjZpBLZtDP7T4KAwItxAy9AZEpGEEZNiJ5HQNiEojFAVhIiIiEjVp8BCRP5/e/cdHlWV/3H8/YVIURRULKhAABvgj5ooCEEHsQIShAQsoOy6sOi6q4jsogSUqCgCCq4EXJcFFAhBqYIFSKSX0KsgQuxiWxCVFnJ+f9ybyUxIMLhICp/X88yTmZM7M/fOyU24H77nnFNaXtUTERFe5cSMGVCxIkyaBPv3w8SJXmXFu+/C7NnetvHx4cM7CjIXRcOGOe/Xq32Ahg1SiH8znp5RPb35Ga68I2wfC7KSRkSpiODkkQDvfPQOEzZOAKBi2YqcWfZMdvywgylbphBXJ46659Vl6LKhxNWJ44YaN/B46uM8EPUAc3bMYfZdswnUCIRVRkRWiqTPvD7HXEmjIBNa5p5DQmGEiIiIiORHgYWInNJyz0UxeTIMGABNmnihRZs2MH++F1KkpeVUT0D48ypVgt69YcgQbwWQvOaiSC8zmL6vRpOeHgi2Zc8f0TOq51FzOoROIOlwTN48mQsqXMDI9JG82uZVvvn5G9olt+Pqi69m6WdLaVWzFf1S+zH9w+ms/mo1j1zzCOedcR5PLXiKnlE9g2EEEDZnRM+onjwY/WDO+/uVHsc7h0RBJrTMPYdEdrvCCBERERHJTYGFiJzSoqO9gKF1a2/J0XXrYNQouOce6N8/PKAIrZ7YvTt81Y7MTC+syPSuzQkE4O23vYkyg+91UTTxS+NJiUsBvFAg/s14+jbvGwwHRqaPpNGFjXgm8AztktvRrGozFnyygLg6cezas4vEhYlcV/069h3ax+XnXs7d9e5m1KpRec4XkT1s4/v93wfbgLAwJDR8+F+GbRR0QkuFEyIiIiJSUAosROSUMXiwF0qcdRYsWOBNhrl7N5Qp481Hkb3U6D33hM89MXw4jBgB06aFrOQxaDBX7IkmgH/x3WwwlIqArEzwJ8tM/qkH1AbwhjgEagR4tOmjtJ7Ymjtq38GMbTNoXrU5/VL7EVcnDsNofVlr7pl2D39v9nc61e3Ea2tfo19MP1rWaBlWFVHr7FoAvLnlzXzni8hr2MZvWfpTwzZEREREpDAosBCREiGvuSh69PDmnPjLX7wAYsMGr2riuuu8oR9r13rDOnIvNbqm/GAWTY5meoo3dOO9nwezfk0EyZ9lEqAPgQDc+3kE/9jQloYNZgXnkHj0/UfpF9OPJZ8u4Z0d7zBu/TgADmQeILJSJBl7Mnhz65s0rtKYCRsn8NDVD1GlQhX6NOsTdqF/X4P7SN6UzPRt04NDMl5e+fIxh2TkNV/EiVr6M7tdYYSIiIiInEwKLESkWMpvJY/4eHj0US94GDsWzKBKFXjwQdhy9mBKr4tmxYoAw4Z521z6cA8eXwbvpIzOWWr0yQisfVuInAUE6NQxgpVnPUrGp0+x5qs1zNk+h/GfPcf1Na+l9cTWRF0UxaovV3FzrZt5acVL7PzvTubsmMPU+KmUP618cELNOTvmkBhIZNDiQcGKh9zVDtmmfjj1uIZk5DVfhJb+FBEREZHizJxzhb0PJ1xUVJRbtWpVYe+GiPyOeowfTPKwaKa/GKBmTbg3cQ6L554LpbJoXa8pixbBtYN6YMDyfqPp2ROGz0zjSMf2XH64E2sHjqZLQhpTSsdSurSREj+RmufUZNa2WQxIG0hV15zPSi0IhhEx1WJY8tkSbrvsNubunMuY28cQe2UsAz4YEDZnRF5zSGS3danXhXd2vBMMIrLnsMgdWuS1jGn25Jx5BQwiIiIiIsWJma12zkX92naqsBCRIi+0msI52LkT9q5sy88V3uWWzjW4MTqSFT98zZFubbgxawgzE5vSJSGNGf/1lv5s0zOOxBGXc/NfN/JB1iHWZo2n2oCtvJ65ihurxFHlQoh7M46ba91M6q5UxrT7Fx3qdCBxYWK+YUT72u3DVtIoyBwSQ5cNDZsbIq+KB1DVg4iIiIgIKLAQkUKWu5rgtmcGE1ktgsiamfRp1oesLJjw+ZP8Y+Jl3HXV3URGwqFDMHv+Hm7524ekfh3F7GX3Uu6mMdxy4b28+1l/qg2Y7oURFeMAmPBTOy77W0veO7SQ8nOT6Hz/VpI/f54utRJ4p89A+qZA9abVg2FE5//r/KthRO6VNI5nDomGFzYMCy0URIiIiIiIHE2BhYicEL91GMPHC6N51sUz7U7vwr/axaeRtGgC1f/9Aj82h6Xbt7CBDZx20xje2raOa0qfxbJPd2B3TeGQi+Pwl3Xg2mFkbotn8cSHiOtzLlO+GEqXWgnMeHggZtDlxeq8/mkijQ4n8OG+aryzu3cweOj7aoDk5TA14vjCiNwrafzWOSRERERERCRvmsNCRH5VQcKIHoPSmBwSPKTtSuOmsW2I2pfIsmG9AK964rRSERzOymTOE304fOQwXZ6dSsqKRURU+pqLzz6Xz37aSdbP5+JqzKNa+Tp8mrmau2s+wjV1L6DPOwM4sPABTm8xmsT6KTz1FFh8PH9t2pMX0pJwi/pS7sZB/LVpT5JWJdHk0xQAllfzJr0cvmI4RzKNu0tPY3Rfbx9zV0Gk7UoLhhG9mvYKHn9EqQgyszKDx6s5JUREREREfhvNYSEiv0le4UREqQjaTmrLrDu9JTx7zOpB8uZkpneaHtzmiivhwMQ7aI8XIAxfOpJSy/7O8kaJdBv7Mw1rV+TjrHls/2kFVfa1psWAAXzx7T52/rCLJjVuZs2npcm4bATldyYwu/dABnzQn0WWSEzpBN74w0DS0sDSv4XrEnErE0j73gsrsgOSSuUq0bt0b250QxgYyDUko+O0sNU2Onfy9jm/Kojcy3pqTgkRERERkZNPFRYip7jcAUXarjTaT25Pp7qdGN12dHAli77N+zJo8SB6RvXkhYXDKVUKXmkznCpnVmHuzrn8c0US1X7qyK7/7iLz4kVEfBFD92bxfPrlQd5etpWLfm7Ll/s/ov6F9Vl/9lM0v/gGlhwayZBrUmjYANqMi+eXhT05vUUS99bqy6jNg2hetieLDybx53NSmDAxp5pixLIkDqy9g2fv6kyv9oHgceSugugxqwcAo9uODh6vKiNERERERAqXKixETjEFGbZRkOoJgCyXxaRNkzh45CBvbX2LO6+6k70H9lK7cm0SFyZS76wYti2tzQP2Vzpd1YG3Ns+gzNQZ3PWX8gyaOwrmPglV1/LLGa3p3rIG337/HCvOjCUmK4GFT91IiwGLWFRqIDFlE2jYANpPiidiegoJtwcYvKASSfSmZ90hjOzSi2HTAjy6MpZy7Y05d+ZMXtmeeLZ92Dl4HHkFEKFBRTZVRoiIiIiIFA+lCnsHROT4DV4ymLRdaWFt2cFDdnv2XAwRpXJyyeiLoolNjqXr1K6s/nI1Axd4S3VeW/VaWk9sTYv/tKD1xNZ0rNOR6yOvZ9z6cXSp14VqW16i4p7r2frdVhJaJPBl5lbu+b+7OTRjOGNHVmb/2Kk0uexSnp85ndPW/JXH72rJ6T82Ytp5V/POnmGsjBhKTFYCiw8m0W7QMBYfTAo+fnxiMi4lhekvBhg4EOo3yqTsgiEccd7klb3aB2gd2Zl6pTqFDduYdmcKtVqkIyIiIiIiJZMqLESKmLyqIHIPbYi+KPqoYRuDFg9iYGAgcVPiiKsTx8RNE2l9WWsS0hJY//V6IitFkrEngwNHDjBl6xQOZh3k/Y/fpwNvcO/F7fjgkgEkLkzkhogEym0LkLo/PrhqRpPDl/P29Fl0KL8Y9l1Bg61/4N/fj6H0levgk2soc3ccZarcQZmkzkwfHU0gAK1aBbh1YF+SmvVn6DWz6NU+QLtBlZh5sDe3VxzCjL5+9cTyeHre1ZmAf7grhvYhLQ3SQ7KIt3uoUkJERERE5FSjCguRQpa7WiI7jMgOKdJ2pZG8OZnJmycz9+O5ZOzJYMPuDRw6cohx68cFqyJuu/Q29h7YS4MLGzBq9SjuuPIOht40lBmdZjBnxxwcjjk75vDu3e/y2LWPkbI5hYeufoj7msbSvtcHjFjmLeu5+NDLJH30D67ZugD7YCANVqbz9twfic76K6kpVwCw8qNdlLtuBBEHqpBw/RNETE9h/hdTGTCAYPAQCHjVEm32zgrOM3E4K5Pbyw7hcFZO9cTQJilkHA6vlAgEoI+mmBAREREROaWpwkLkd1KQSgnIGcoxs/NMrrrgKrZ9t41DRw4xfv14tn63lVVfriKuThwAsZNjuaHGDSz4ZAGj2oxi67dbeW7JcyS0SGBgYCBpu9IYuWpksDKizNaudG7Sip5RPYPVE1OmwPj9XjgxcvlrfHjkMn6ptopSI9L54N1IMr+L5rQ601ix+UeuvQzWfRDJ0FdjyDw/nZ9qQGIiNHoonR3TpjH9xQCBAAQCAWIfSWHbpelAzvGuGBqeOsx54ugUolf7QDDQEBERERERyabAQqQAcocPBVmRIvewjdnbZzNh4wQcjgplKlCxXEU+/uFjpmyZQvNqzWkzqQ3XRV7Hkk+XMPyW4Wz/fjtDlg0JhhEA1StVJ3FhIgktEqh6VlUeff/RYDixdmklFtmg4DKfgcgAbV+P5z9P9uX0m5Po2+Qphr6VxvxPf6Tx4XQ4EknUR92YcvgJ7r6+JTXqR/L005CQ0JZAtwo8M3YhTw9sQkKCFyqkpQWIT4KEBBg6tA+JieHVFNNfDJCeruBBRERERERODAUWcko5UStpRJSKoPf7vRly0xAA5n48l4mbJuKco/LplalQpgIffvch+zP3M279OLZ+t5XVX63m0SaPct4Z5zHggwE8EP0Ac3bMYfZdswnUCNA/rX8wjLj0nEt5PPXxYBixe3mAK66EpB1eZcQLC4fzwsIRdC0zjYEBL5y4eXwbSE3ENQnwdXlInxLg0OtvcuSiZewfns6yOpFkHTqXsk1eZvu8dtxGJKvn1WDoq39i2750Rg3ywoikJKhUKcD6kYGQxzBoEKSk4FdUQHw8NGwYHloElFeIiIiIiMgJosBCSoyCVEHkDh56zOpB8uZkpneaHnyd3Nuk7kzlmUXP8KdGf6JdcjuaVm3Kok8W0apmK/ql9mP6h9NZ/dVqHox+kAvOuIBnFj1Dj8Y9gvNFpGWkBYOI7EqJb3/5NtgWqBEgbVcaSatywohhS0Yw6+6cJTxvGx/LgZXG0Kun0SsQYO7S3Szfl4yLKMXatfDe5AA2dhPV6nxFmzZw/fWwdCncNWgd995yDWn/iSQxERISHiTQrQ7PVEgncaAXSDSsFGBQ90AwjKhUCXr3hiFDoFcvr61NG46qqEhJ8SbGVEghIiIiIiK/BwUWUiz9liqI0JU04t+Mp2dUT5I3J4ODXXt2cXDHQeZ+PJdRq0fRrGozWk9sTdRFUaz6chXdG3WnZY2W/Hz4Z/615l/0i+lHYsvEsKqI7DBi78G9wTYgGEQkrUoiEBk4qi33UI4123czOyOZYcMg8DKQESBr4500iDyHp+4LMPufsH7ZaBpf25exGZ+yZz3MmwdzptTghhtq0L8/fjgBA3v+jbQ0r0oiv+qJ3btzKicAMjO9sCLTmxeTQADefjt81Y7sdoUVIiIiIiLyu3HOlbhb48aNnRRfzy9+3qXuTA1r6z6zu+s+s3vwcerOVFdxUMVgW+rOVFd5cGU3dOlQV3lwZZeQmuAqD67snl/8vDv7ubNd16ldXYVnK7j7Z9zv+qf2dzFjYhxP4mLGxLges3q4M58903Wb3s2d/dzZbu6Ouc455xJSExxP4hJSE8LeI/u1c79X92dT3dCpOduUe/IsV+7Jiq77s6nB55+WcJYr079i8PhSd6a605483Z3WYqhLTXUuM9O51193rky19S6iVpqLiXGufHnnunZ1bswY57p1cw6cS/B2ySUkhD9OTXWucmXvceXKzg0d6n1N9T/OoUOdM/O+hm6fGv5xi4iIiIiI/G6AVa4A1/aqsJBCVZBKiexlPQ2j81Wdg9tmuSwmbZrEEXeElM0pdKnXhb0H9lK7cm0SFyYSUy2GQ0cOEVMthvEbxvNA9AMMuXEIyz9fHraSxlPXP8X5Z5wfrIpoVatV2BCNvKog1i6txKPv96ZNxBAGBnodc9hG6fL+gWUEYHNnHHDk4wDbD8PiyQFKjdpAtTpf07o1REfDmjUw/IV6ZGTA88/7lRIDIS3NW+ozdF6J8MqJo+eZyD2UI6/qCQ3tEBERERGRokiBhZwwJ2IljdBhGx2ndCSuThyTNk3i/ob38/3+78OGacTViePbX77l32v/zZ8a/YmnWz7N2q/WhoURsVfGsvTzpcHHtc6uxaDFg0jpmLOSRuzkWAw75mob2RNa0jQANcCVyoT3huDa+lf+GQHcps5c0wAGdQ+wZy18NHI09/bsypgpn/DZIpg/H+6M8467XTu48UZYsACmTazFrbfWChvKccUV3tf8woiCzjOReyhHn6NXFdXQDhERERERKZIUWJzi8qpwyB0qFCR4gILNIZFdKdGhdgcuPfdS1n+9noNHDgZX0sgOIvYe2EujKo0YvXo03Rp0o1fTXlxY4UKqVayWM1llZID4N+ODQcOVla8MCyMqlasUfP9eTXsFg4f7ayYGjzc5GQ4dMuqV6sTAwMA8wwkyApSf9jYxndKJj4eePWFFUh+G9vVChL/vgVdfhcf+MppywHu1veAgJgaurtKMzCuaMWEC9OvntQNUr54TTtx6K2HzTAwfDiNGwLRpx1cpoXkmRERERESkJFFgcYrJHVDkVeGQe/jFsYKH7G1CKyPipsTRtX5XxqwdQ9f6Xemf1p/pH04PhhEA7VPa06pGKz745ANebfMqW77dwnNLngtOXpm2Ky2sUqJLvS5s/357cJjG8BXDGbFiBNM6TQurgggNI+alZtK2zBDmpWbSqykEagS4v/zbvPafdOIu8S7kvyCdA+Om0ekv/lV9HuHEyJHwWlKAKlUCvLA8J4zYswdq14bBgyEuDu68Ez77DF56Kacy4sABeO+9nMctW3pvc6yhHLt3e0FKNlVKiIiIiIjIqUiBxSkm+qJo4t+MD1YhADgckzdP5oIKF5C0Kim4xGf2ShpJq5IYctMQBi0exJ4De3gl/RVevOlFvvnlG9pOakvjixqT/kV6sDKi7nl1eXH5i3Sq24leTXtx3unnMWTZkLCVNKpXqh6slLjkrEvo9X6vYDhRqVylo4Zt3DY+ltKlLbjU53tLdrPhSDLJyRDom3cY0ap8n+CwCfCqGKa8EOC5voGjKiWefRY++ggmToSuXQOcvT/Aj36lRIsW8P33sGsXLFoEjz/uVVTExsLWrTnBQ5Mmvz5sIzYWzI5dPTF6NHTuHD6vhMIIERERERE51SiwKKZ+y3wR2e648o6wMGJ6p+mkZaSRuDCRvs37Ur1SdT7d+ynNqjYLTl4ZOpllq5qtOLPsmdQ5vw67f9rNSyteyrcy4uqLr2bs+rH5Luv5wsLhDFsyIhhEBCID3DS2DVH7ciolAjUCNIjoTPpqoJk3TKPT6aNZ+c/OfPGndCCQZxiRlOSFBc8+C59/DmPGwMMPe59B7ZBhG3v3Qv36MGoU/OEPMGAAbNgQXgXxyy/wwgvw1ltecHDuub8+h0RewzY6d865n/1VQzlERERERESOpsCiCCpIGHE880VkD9uYv3M+8W/GkxhI5Pv93wfDiLHrxjJlyxRiqsUwfMVwslwW559xPgs/WUjf5n3515p/EXtlLFu/2xoMHubNrMwVV+7njR1vBNvmzqrEugqDmNMt/5U0bv5PLGbGu/d5AcWa7buZnZHMsGEQeBnICFDmrbdZd2E6aWneRXtaGux4aTSD+xIWRgztG+DZZwM8+p0XRvTpA2eeCXXrhocRdevCiy9Cp07QoQNkZIRXRsTGegFF9uO6dX/bahsFGbYxevTRbQonREREREREjqbAopAVZFnPvMKI7PkiQislEgOJJC5MJP3LdGZtm0XHOh1xzoWtrNHYdWfNlr3M/3o+j137GCOWjiL90w10LTOb0d28uShyhwobl1f+1SU8K+0J8OieNpRb5F/V57OSRvaynmR42zx6+WjSXu7MvAvT6d8/QFISvJ0SwLkAHTt6IcOECfDgg3D48NGVEXXrwrBh3hwSN9zghRGbNoWHEVu25Dy++mqttiEiIiIiIlIcFJvAwsxuAYYDpYHXnHPPFfIunRAfL4zmWRcfXEIzbVcaT7wziAY/5YQRwxYmcdtpz9Hv/adZ9/U6pn04jYv/24kJb+2ldl1vmEYNi2Hl0vJccvgGkjcl8/A1D/PTtCGUojS9O+fMF/FdeoCkLfEMbTKVXjcGWLRyL8v3JVO6vL9DeYQKBVnCMykpwNBX32bbFXmvpNF/vzd55aTRo9mzxwsSWraEuXOhY4cAGRmB4HwRCxZ4b9O4sRcydO3qDdXYvt0LFvILI7LnkJgypeBhhFbbEBERERERKZqKRWBhZqWBV4Abgc+BdDOb6ZzbUrh79r/r3CRA8iMpxLo4Ol7VjuSNUziy8R7WHtjDFVW9MKJmqRhmv5tJ3ZtieH3D68RWeZD5Lwwh66JlRJzjzRcxbFESM2fGcsYtC0hokcCIZUkcXnI7BkRUTwq2HVi7m57RKcGgYUfSaHo+1plx89Kp/JNX4fBeijduIb/gISkJpo0fzVVXQeInXgDQoQOc8U2AyB8C1KmTM1nljz8SfHzddd4KGBdcAO3bw7hx8NhjcMstXiVFdvDw5JPeZ/PKKzlt9esff2XEbx22oXBCRERERESk8BWLwAK4GtjhnNsJYGbJQDug2AcWgQBMfzHAbcP+yJjMwZTd2J23HniW7fvW8NjKJGLKJrB4fxK33xrLrL1LiSmbwIydSfx5eE0mfjYIl5ICBwK4pZXg5t64hUMgsxduZgDrHAsYLmWat83MAGU7dqb1rXdT7mvv4v6Pf4QOjQN8m+5VONx0EyxeDEeO5AQN2cMvQodjbNgA8+d7y2927QozZ3qhQ2SkN0QjO2ho1y68CqJ2be+4Z8/22oYP91bcCF01oyAraSiMEBERERERKdmKS2BxMfBZyOPPgWtCNzCz7kB3gGrVqp28PTsRItOw+m/A7JexBtN4f9c7jF+TTMt985g/sT71OkQz002mzuE3WDTrZqJu6sJr68ZxQ7Xp/HxWMxIToUaLa7js0yV8dDjLr24I8NPmNwCoUDEQbKv1wzKefvYTNs7ygoEpU6BcOZg3Dx56yJsv4rHHoHTp8AqH3Et4xsZ6FRIzZuRMjJk7aCjIsp67d3uhR7aCrqShMEJERERERKRkKy6Bxa9yzr0KvAoQFRXlCnl3CixtVxrtJ8UTMeMtOlzRgjlzWzD6QAK3XnI3C5Lrc//98Mbmb2nZtCVLV+7ikUdg3LjLeOqfN7LzwFKmT2vmhwjNuLkdrJmZEyqkPNkW8IZ25FQ81GTW6zWZNcu7uB82LDxUaN++YMFDXhNT5g4aCrKs5+jRXlt6enhbbgojRERERERETi3FJbD4Aqga8vgSv63YS16UjktJYcaIFn6lQj3aPPQw73+Zzhw/MKg97A9hgUHbthAbex1m1x1XNUNBh1YUJHjIa2LK3EGDlvUUERERERGR38qcK/rFCGYWAWwHbsALKtKBu5xzm/PaPioqyq1ateok7uFvN3gwREeHX7D36OF9zb64HzwYIiK8wCA7BPgt24A3dCM9Pe8wQUREREREROT3ZmarnXNRv7pdcQgsAMzsNuAlvGVNxzjnnslv2+IUWIiIiIiIiIicSgoaWBSXISE45+YAcwp7P0RERERERETk91eqsHdARERERERERCQ3BRYiIiIiIiIiUuQosBARERERERGRIkeBhYiIiIiIiIgUOQosRERERERERKTIUWAhIiIiIiIiIkWOAgsRERERERERKXIUWIiIiIiIiIhIkaPAQkRERERERESKHAUWIiIiIiIiIlLkKLAQERERERERkSJHgYWIiIiIiIiIFDkKLERERERERESkyFFgISIiIiIiIiJFjgILERERERERESlyFFiIiIiIiIiISJGjwEJEREREREREihwFFiIiIiIiIiJS5CiwEBEREREREZEiR4GFiIiIiIiIiBQ55pwr7H044czsW+CTwt6PAqgMfFfYOyH/M/VjyaG+LDnUlyWD+rHkUF+WHOrLkkH9WHIU176s7pw779c2KpGBRXFhZqucc1GFvR/yv1E/lhzqy5JDfVkyqB9LDvVlyaG+LBnUjyVHSe9LDQkRERERERERkSJHgYWIiIiIiIiIFDkKLArXq4W9A3JCqB9LDvVlyaG+LBnUjyWH+rLkUF+WDOrHkqNE96XmsBARERERERGRIkcVFiIiIiIiIiJS5CiwKARmdouZbTOzHWb2j8LeHwlnZlXNLM3MtpjZZjP7m9/+pJl9YWbr/NttIc/p6/fnNjO7OaRdfV3IzCzDzDb6fbbKbzvHzOaa2Uf+17P9djOzEX5/bTCzRiGvc6+//Udmdm9hHc+pysyuCDn31pnZj2b2sM7L4sHMxpjZN2a2KaTthJ2HZtbYP893+M+1k3uEp4Z8+vEFM/vQ73YWnpoAAAsySURBVKtpZlbJb480s/0h5+aokOfk2V/5/UzIiZdPX56w36dmVsPMVvjtk82szMk7ulNLPn05OaQfM8xsnd+u87KIsvyvP/S30jmn20m8AaWBj4GaQBlgPVCnsPdLt7A+qgI08u+fCWwH6gBPAr3z2L6O349lgRp+/5ZWXxeNG5ABVM7VNhj4h3//H8Dz/v3bgHcAA5oAK/z2c4Cd/tez/ftnF/axnao3/9z6Gqiu87J43IAWQCNgU0jbCTsPgZX+tuY/99bCPuaSeMunH28CIvz7z4f0Y2TodrleJ8/+yu9nQreT1pcn7PcpkAJ09u+PAnoW9jGX1FtefZnr+0OB/v59nZdF9Eb+1x+n/N9KVVicfFcDO5xzO51zh4BkoF0h75OEcM595Zxb49/fB2wFLj7GU9oByc65g865XcAOvH5WXxdd7YBx/v1xQGxI+3jnWQ5UMrMqwM3AXOfcD865/wJzgVtO9k5L0A3Ax865T46xjc7LIsQ5txD4IVfzCTkP/e+d5Zxb7rx/kY0PeS05gfLqR+fc+865TP/hcuCSY73Gr/RXfj8TcoLlc07m57h+n/r/a9sSeNN/vvryd3SsvvT7Ih6YdKzX0HlZ+I5x/XHK/61UYHHyXQx8FvL4c459MSyFyMwigYbACr/pL37Z1ZiQkrj8+lR9XTQ44H0zW21m3f22C5xzX/n3vwYu8O+rL4uHzoT/40vnZfF0os7Di/37udvl5PsD3v/aZathZmvNbIGZxfhtx+qv/H4m5OQ5Eb9PzwX2hARZOicLTwyw2zn3UUibzssiLtf1xyn/t1KBhUg+zKwC8BbwsHPuRyAJqAU0AL7CK7GToq+5c64RcCvwoJm1CP2mnzJruaRiwh8HfTswxW/SeVkC6Dws/szsCSATmOA3fQVUc841BHoBE83srIK+nn4mCoV+n5Y8dxIe8Ou8LOLyuP4IOlU/fwUWJ98XQNWQx5f4bVKEmNlpeL8sJjjnpgI453Y7544457KAf+GVQkL+faq+LgKcc1/4X78BpuH1226/NC67DPIbf3P1ZdF3K7DGObcbdF4WcyfqPPyC8GEI6tOTzMzuA9oAd/v/oMYfPvC9f3813lwHl3Ps/srvZ0JOghP4+/R7vPL0iFztchL5n/8dwOTsNp2XRVte1x/ob6UCi0KQDlzmz55cBq+0eWYh75OE8Mf7/RvY6pwbFtJeJWSz9kD2bMwzgc5mVtbMagCX4U1qo74uZGZ2hpmdmX0fb3K4TXj9kD1r8r3ADP/+TKCrP/NyE2CvX4b3HnCTmZ3tl8je5LfJyRf2v0U6L4u1E3Ie+t/70cya+L+/u4a8lvzOzOwWoA9wu3Pul5D288ystH+/Jt45uPNX+iu/nwk5CU7U71M/tEoDOvrPV18WjlbAh8654DAAnZdFV37XH+hvpVYJKYwb3qyu2/FSzScKe390O6p/muOVW20A1vm324DXgY1++0ygSshznvD7cxshM+6qrwu9L2vizVq+Htic3Qd442vnAx8B84Bz/HYDXvH7ayMQFfJaf8CbaGwH0K2wj+1UvAFn4P3PXcWQNp2XxeCGFzJ9BRzGGzf7xxN5HgJReBdXHwP/BKywj7kk3vLpxx1446Wz/16O8rft4P/eXQesAdr+Wn/l9zOh20nryxP2+9T/+7vS//mYApQt7GMuqbe8+tJvHwv8Ode2Oi+L6I38rz9O+b+V2T+IIiIiIiIiIiJFhoaEiIiIiIiIiEiRo8BCRERERERERIocBRYiIiIiIiIiUuQosBARERERERGRIkeBhYiIiIiIiIgUOQosRERESiAz+8DMok7C+/zVzLaa2YTf+73+F2Y21sw6FtJ7x5pZneN8TkMz+7d//z4zyzKzeiHf32Rmkf79eWZ29oncZxERkaJAgYWIiIiEMbOI49j8AeBG59zd/+v7mKck/tskFjiuwAJ4HBgR8vhz4Il8tn0drx9ERERKlJL4jwIREZFiwcwi/eqEf5nZZjN738zK+98LVkiYWWUzy/Dv32dm081srpllmNlfzKyXma01s+Vmdk7IW3Qxs3X+/8Zf7T//DDMbY2Yr/ee0C3ndmWaWCszPY197+a+zycwe9ttGATWBd8zskTyObZGZrfFv1/rt1/vtM4Et/nbbzGw8sAmoamZJZrbK/0ye8p/X0symh7z+jWY2LY/9bGxmC8xstZm9Z2ZVCrqN/5m/6L/3VjOLNrOpZvaRmT0d8vx7/M9vnZmNNrPSfvtPZvaMma33++IC/7hvB17wt6/lV6VsMbMNZpacx/6dCdRzzq0PaX4bqGtmV+TeHpgJ3JlHu4iISLGmwEJERKRwXQa84pyrC+wBOhTgOVcBdwDRwDPAL865hsAyoGvIdqc75xrg/e/7GL/tCSDVOXc1EMC7kD7D/14joKNz7rrQNzOzxkA34BqgCfAnM2vonPsz8CUQcM69mGsfv8GrvGgEdCK8WqAR8Dfn3OUhn8FI51xd59wnwBPOuSigHnCdPxQiDbjSzM7zn9Mt5Jiy9/M04GX/GBr733/mOLc55L/3KGAG8CDe532fmZ1rZrX942nmf7ZHgOzqkjOA5c65+sBC4E/OuaV4gcJjzrkGzrmPgX8ADZ1z9YA/c7QovPAmVBYwGK/yIoxz7r9AWTM7N4/XEhERKbaOp+RTRERETrxdzrl1/v3VQGQBnpPmnNsH7DOzvcAsv30j3kV+tkkAzrmFZnaWmVUCbgJuN7Pe/jblgGr+/bnOuR/yeL/mwDTn3M8AZjYViAHWHmMfTwP+aWbZF/WXh3xvpXNuV8jjT5xzy0Mex5tZd7x/p1QB6jjnNpjZ68A9ZvYfoCnh4QzAFXjhwlwzAygNfHWc28z0v24ENjvnvvKPeSdQ1f8sGgPp/vPL44UzAIfwKiHA68sb8/5o2ABM8CtGpufx/SrAt3m0TwSeMLMaeXzvG+Ai4Pt83lNERKTYUWAhIiJSuA6G3D+CdwEMkElOJWS5YzwnK+RxFuF/212u5znAgA7OuW2h3zCza4Cfj2vPj+0RYDdQH+84DoR8L/f7BB/7F+O9gWjn3H/NbCw5x/8fvHDmADDFOZeZ63UML2Roeoz9+rVtQj/L3J9zhP/8cc65vnk897BzLvszP0L+/85qDbQA2uIFEP+X61j2c3Sf45zLNLOhwN/zeM1y/vNERERKDA0JERERKZoy8P4nH+C3rm7RCcDMmgN7nXN7gfeAh8wvDzCzhgV4nUVArJmd7g8fae+3HUtF4CvnXBbQBa+SoSDOwgsw9prZBcCt2d9wzn2JNwSlH154kds24Dwzawre8A8zq/sbtjmW+UBHMzvff/45Zlb9V56zDzjT374UUNU5l4YXPFQEKuTafitwaT6vNRZoBWQPjcHvywvxfmZERERKDAUWIiIiRdMQoKeZrQUq/8bXOOA/fxTwR78tEW+4xgYz2+w/Pibn3Bq8C+WVwArgNefcsYaDAIwE7jWz9cCVFLB6w59oci3wId4QiCW5NpkAfOac25rHcw/hhTvP+++7Drj2eLf5lf3bgheYvG9mG4C5eEM4jiUZeMzvi8uAN8xso3+cI5xze3K9x4dARX/yzbyOcQRwfkhzY7y5M3JXnIiIiBRrllO5KCIiIlK0mdk/gbXOuX8X9r78nvxVV/Y5514rwLbDgZnOuaNWdxERESnOVGEhIiIixYKZrcabVPSNwt6XkyCJ8Dk0jmWTwgoRESmJVGEhIiIiIiIiIkWOKixEREREREREpMhRYCEiIiIiIiIiRY4CCxEREREREREpchRYiIiIiIiIiEiRo8BCRERERERERIocBRYiIiIiIiIiUuT8PzP6fhsv+Oz0AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 1296x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# fit a quadratic curve to our first query\n",
    "coef_1 = np.polyfit(df['keys'], df['time_1'], 2)\n",
    "p_1 = np.poly1d(coef_1)\n",
    "# fit a straight line to our second query \n",
    "coef_2 = np.polyfit(df['keys'], df['time_2'], 1)\n",
    "p_2 = np.poly1d(coef_2)\n",
    "\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "fig.set_size_inches((18, 10))\n",
    "ax.plot(df['keys'], df['time_1'], \"bx\", markersize=6, label='query 1')\n",
    "ax.plot(df['keys'], df['time_2'], \"gx\", markersize=6, label='query 2')\n",
    "ax.plot(df['keys'], p_1(df['keys']), \"b-\", linewidth=0.5)\n",
    "ax.plot(df['keys'], p_2(df['keys']), \"g-\", linewidth=0.5)\n",
    "ax.set_xlabel('number of array elements (N)')\n",
    "ax.set_ylabel('query duration in ms')\n",
    "ax.legend()\n",
    "\n",
    "ax"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}